|MadSci Network: Zoology|
In general I don't think we know "how" animals can avoid being made ill or dying from consuming poisonous plants. We may infer that the ones who ate the toxic plants did not, for the most part, live to reproduce. in the case of deer, according to the sources I found, there's a general consensus that deer do eat poison ivy (study in Arkansas of deer habitat in the Ozarks) but are not poisoned by it. Their immune systems are different from those of humans, so it's not a problem for a deer to eat poison ivy.
Perhaps our "hairless skin" (see the "Naked Ape" by Desmond Morris for amplification about humans' unique characteristics and how we have survived in nature, perhaps, despite them) makes us prey to problems that animals with fur or more body hair do not experience.
Coincidentally, a local park ranger was showing a native Georgia possum to my students and pointed out that possums have a broad immuniuty to many toxins including poison ivy and snake venoms that affect humans, and the proteins the possum can develop to avoid harm are being studied in hopes of developing antitoxins for humans.
Here are some interesting web sites about poison ivy:
http://www.birchisland.ca/poisonivy.html ("Deer immune systems are different so poison ivy has no effect on them.")
Try the links in the MadSci Library for more information on Zoology.