How do I find out if my beagle is of enough quality to become a showdog?

Go to http://www.akc.org and check out the breed standard for your Beagle. In addition if a Registered Member Breeder (with the A.K.C. or the C.K.C.) sold you this pup, the breeder would have told you that this pup was potentially show quality and the price you payed along with your registration papers you signed and received from the A.K.C or the C.K.C. would have determined such. You can show an altered dog in certain classes, so just because your pet has been spayed or neutered, don't let that disuade you from seeking out shows that offer altered classes. Just because a breeder is a member of the AKC or CKC does not mean that they are ethical. Those points made (in disagreement with the first two answers given to this post), your best bet is to find a good, ethical, show breeder who is willing to mentor you - or at least take you under their wing for a time. Go to shows. Good luck!
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Any dog can be a showdog.and beagles are very smart dogs too.I think you should see how it goes and just remember it will take a lot of time and patience!!
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I have 2 very obedient dogs myself

The easiest way is to show him once he's old enough. Do a bit of show-ring training with him before the first show, and read up on how to show Beagles. If you have the possibility visit a few shows without showing first, that way you can see how it's done and get a feel for it.

Getting a show mentor to help you (ask your breeder) can be invaluable.
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Not a show person, but was under contract by the breeder to show my first dog at least twice.

Your breeder would be a good reference - he/she should know what makes a good show dog. (But, if he really was a good prospect - they probably would only sold him to another dog show person for big $$ or kept him themselves to show.) Sorry to sound negative - I'm sure he's the cutest thing to your family. Also, contact your local beagle club - the AKC website lists the National breed club and the local breed clubs state by state. If you are going to show, you will need to learn how to do it properly from experienced show folks. So that means you will probably be joining the state or local beagle club in any case. They can tell you if Rocky's up to standard. Good Luck!

Recommendation is still the same (Aussie or USA) - go to the shows, investigate the local clubs and ask someone to evaluate your dog. Ask a club officer - they often are older and very experienced.
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The question is, how good is Rocky?

Your breeder should be the one to tell you. If your breeder shows (as they should) go back and talk to them, and have them evaluate Rocky.

If there's an issue with the breeder, start attending shows and talk to the people showing. Take Rocky along. After the judging, ask them to go over him and tell you what they think. Please have a thick skin, as if he wasn't sold to you as a show pup, it is unlikely that he is.

However, I suggest you take handling classes with him, and learn on him no matter what his quality for showing. It will prepare you for your next dog which you can buy specificially to show.
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Duh….ASK an exhibitor to EVALUATE! AT 6 MONTHS!

At 8wks.,there's NO WAY to know how CLOSE it is to the breed standard!
Conformation dogs must NOT "sit" in the ring! They're STACKED & GAITED!
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OMG stay away from that whole show dog scene if you are any type of normal person! To begin with showing dogs is VERY political. It is rare for people to just walk in to the circle of showing dogs. You are usually entered by association. The judges are very tight with breeders and it would be rare for a newcomer to win when you are up against someone who has been showing dogs for a few years and knows the judge.
Plus you have to have a handler and that is very expensive. It is very expensive to show dogs and a huge financial loss. You have o travel non stop and pay a handler and you have to do so many shows a year to stay in the actual “Showing dog” business. You cant really do it as a hobby.
Also AKC/ANKC means nothing to these people. I mean of course they have to hold those papers, but that means nothing at the end of the day.
So I used to work for a family that owned a Vet clinic and his wife was a handler that showed their German Shepherds. Their grown children worked at the Vet and were the biggest geeks I have ever seen and they were really into showing dogs. They and all their friends would laugh their azzes off and my AKC beagle because she was not of show quality. This family and the entire show dog group (Which is thousands and thousands of bizarre people) didn’t understand that the average person thinks an AKC beagle is just the same looking dog as a champion beagle and vise versa with every breed.
Anyways, I am a dog lover and I don’t have children yet so my beagle is like my child for the time being. I was invited to a big dog show that came into our city and I was excited to see what it was like. They even told me I could bring my beagle and she could hang out with the other pups up there. So I show up with little beagle and she is all wagging her tail and so excited and I could not believe the responses I was getting from complete strangers that call themselves “Dog Lovers”! I was getting stares, points, laughs and ugly faces. I saw the girl that I worked with and went over to her and she was standing with a woman who was some top handler, named Malerie and Malerie said to me (She didn’t ever introduce herself).. “Dear God, is that a beagle that you are holding?” and everyone started laughing hysterically. I could not believe it. How weird and terrible that these people were judging my little, sweet, friendly, cute beagle! So I put my beagle down in the pin to play with my co-workers dogs and about five minutes later some dog groomer comes up to talk to some of the people hanging around and goes “EWWWW, what the hell is that?” pointing to my beagle and being all dramatic. People were laughing so hard. My co-worker was like “Oh that’s my friend’s beagle.” And the groomer said “Oh my gosh, that scared the life out of me. I actually thought someone was going to put that ugly thing in the ring!” People were laughing and I was just in shock that this is how these educated, wealthy people who are driving BMW’s and have ½ a million dollar RVs outside were acting.
Needless to say I wasn’t rude but I told my co-worker I needed to leave early and I was very polite and took my beagle and left and people were pointing. MY GOD, you would have thought I had a dog with no head or eyes because of how people were acting. I was honestly in disbelief because of how these ADULTS were acting, all snooty and rude and my freaking little beagle. Give me a break and get a life.
As I left I couldn’t help but laugh actually because these people were so clueless. They really judge an innocent animal on whether or not the animal is of “High standards.” It’s a freaking dog, a companion! Plus its not like these people did anything great, they just drove somewhere and purchased a dog that was of “Show quality”.
When I got back to work the next day I was talking to one of the girls is a Veterinarian that works there about how weird it was and she said “I KNOW!! It is the weirdest environment I have ever been in. That’s why I refuse to go to any of those ridiculous events. I prefer a good ol’ mixed breed because I AM really an animal lover.” I was just so shocked on how weird the whole thing was.
I enjoy people and want a family and like “Human contact.” The people that show dogs are all about dogs and that’s it and they truly lack people skills.
If you haven’t watched the movie “Best In Show” I truly recommend it, because it is no joke. That is really how people act.
Go figure!
Good Luck, and I am really not trying to be negative, I just couldn’t believe how bizarre the whole experience was. It may be totally different for you.

Here is a picture of my "Ugly" beagle: http://i140.photobucket.com/albums/r38/rcallejas/bella2.jpg
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Went to one of the weirdest experiences of my life.