The answer is... I don't really know. Two course moderators said that it seems fine here. But I also asked on a Facebook group dealing with correct Polish language, and all the comments said: you should use plural. Now, I may have not chosen the best example, because I asked about "my brother and my cousin". They argued that I have to say "moi brat i kuzyn" or otherwise it seems like they are one person (jokes about rednecks, anyone?)... Now, of course my dog and my cat aren't the same thing. But I really don't know if your version would be correct... sorry :(
BTW, to me this 'moi' thing doesn't sound well... I guess that actually this is not a construction that you use often, for example you'd be more likely to say "moje zwierzęta" instead of dealing with the dog and the cat separately. But it sure is an interesting problem.