I don't mean to get Mark Steyn all excited but a reader writes:
We also have a rescue dog, and were told by the shelter that she is a mix of beagle and rottweiller. Our term for that (and as far as we can see, the only term for that) is Beguiler. Our other dog is a potcake.
Beguilers, puggles, bagels ... all very post-breed, aren't we?