Animals are able to sense something wrong with zombies, unlike thier human companions. And so most animals will know to get away way before we would. This prevents any real known cases of animals getting turned.
However, there are conflicting facts given on this subject. I have read its safer to have a dog with you when you are finding your hiding spot. They can slip past zombies easier than you would, perhaps locate food for you. But of course the facts are not all in on this one. And you might be sending your best friend to his death. Or he might not risk coming back. The survival instinct with still exist in Fido now matter how fond he is of you. Odds are, you slip him out of your fortified basement complex. And you are never going to see him again.
I'm not too worried about a zombie animal. If they are like the slow shambler zombies I have seen they wouldnt be much of a threat. Unless your talking about rats, birds and other small animals. That would suck.
Well there's a zombie strain of malaria in cambodia (no, really, check it out: http://22.214.171.124/south_asia/4483241.stm.htm ), so does malaria infect animals? I know mosquitoes carry the parasite without being harmed, but they are insects...