I am no animal expert, so consult an expert if you do need to do that for any reason.

If it's only as a food for thought, depending on the mammal you'd probably be fine unless whatever animal has a very prominent feature you need to worry about. Farm animals have prominent features (cow produce lots of milk, sheep produce lots of wool) that most likely unbalance things a lot compared to us. Other mammal like cats and dogs probably have a balance close enough that the variation between their RDA and ours should be fine.

If you look at anything other than mammals, things change drastically. Hollow bones and feathers in birds, cold blood and scales in lizards, etc... are probably much further away from us.

Again, not expert on this subject, consult an expert if you're planning on putting your dog on the same diet as yourself.