Rabbits are good. However, they are subject to

There are two common ways that humans can contract tularemia:

From the bite of an infected tick, deerfly (Chrysops discalis), or mosquito. When transmitted to humans by insects, exposed body surfaces are bitten, and the on set of pain and fever is sudden.
When broken skin (cuts, abrasions) comes into direct contact with an infected rabbit carcass (namely rabbit species of the genus Sylvilagus which are the cottontails). Many other wild creatures carry it, too.

One more thing: Rabbit flesh is very very very low in fat. That should be added when the rabbit is cooked.