|DNA, courtesy of Wikipedia|
The first class is just a basic grounding in genetics, nothing really special about dogs (although I use dogs for many of the examples). So if you have a solid or even just passable genetics background, you don't need to take that. If you're not sure you could explain what a gene is or what a chromosome is, though, you would probably be a bit overwhelmed in the second course without having taken the first one.
The APDT is an organization that I've respected for quite a while, so I'm thrilled to be working with them. If these classes are well-received, they will repeat periodically, so if you can't take one or both this summer, you should get another chance later.