Most artists can work off pictures and ideas. You don't have to be able to draw things yourself. If you say you want a Chihuahua character drawn, it is very unlikely that an artist would give you something that looks like a German Shepherd instead. Even if you didn't give reference images for the breed, people should know how to work Google Images on their own.
It can vary slightly depending on the skill of the artist though. There are some artists who know how to pay closer attention to both obvious and subtle differences in dog breeds, and there are some artists who will always draw every canine character to look something like a wolf. It's important to look at an artist's past work and see how well they differentiate between canine species.
As long as you specifically point out that you want it to look like a certain breed though, the artist ought to be able to understand.
