|Think about Loose Coupling|
Polymorphism is a much more general concept, and we skip over that generality by starting with the factory piece first.
See my reply below for why this isn't a good example of polymorphisim anyway. Update: blue_cowdawg's update fix the OP's polymorphisim issue.
I would be interested to see if the factory could be made without using eval, as well...I think it can, especially if the dogs were loaded previously in a more-safe matter.
It can using require $path_to_breed; instead of eval "use $breed;";. But it ammounts to almost the same thing, except that you have to specifiy the path to the breed file instead of the traditional 'module::name' format. As you say, it's also possible to load all the subclasses before anything is called, but that could get very inefficient fast.
My favored solution would be to map a breed via a hash:
Note: All code is untested, unless otherwise stated