Hey Jim,
I think what you've done is an excellent way to get started in pet portraiture. So I'm not going to get into a lot of detail in this response other than to say that if you are good, the more portraits you do, the more you will get to do. It's axiomatic but absolutely true.

As for breeders and dog shows, there are some additional things you need to know. If you've never shown a dog, it's hard to know how they should be stacked and from which angle they should be shot. Most breeders want their breed positioned and photographed in particular ways. You need to know the "head" breeds so you know what to feature about those dogs (heads obviously). In short, you need to really understand each and every breed so you can emphasize what the breeders want to see.

The dog show world is all of the above plus a lot more. If you want to become a dog show photographer (the guys who take the win shots at shows) you need to know all the breeds intimately and how they should be stacked and from which angle they should be shot. You also need to be able to sell your services to show chairmen. This is a highly political process not unlike the entire world of dog-showing. Once you've been able to get a show contract, you need to be able to do the work: cover 8-10 rings simultaneously when they finish judging a breed when they all finish at approximately the same time. And then you need to understand the business end of what you do with those images in order to get paid.

The shooting part is not as easy as it looks and you have to have credibility with the handlers who can make or break you in the ring. So, unless you have experience as a show person, you might want to think twice about this niche.

On the other hand, great pet portraits require good technique and a good eye for how those pets should look and you clearly have both of those talents. And, frankly, that's where the $$$ potential is although the market is harder to identify and promote to. But, as I said, you've made a good start.

Jim