Well, for starters, the end of the first AP book includes some really cool, new options for weird animal companions: the enchanter heron, the gliding turtle and the sea crawler.
I like to keep most of the island as something exotic that doesn't have all the same animals, but since there are boars, it's easy to add a few more animals. Based on the warm climate, forests, and presence of boars, here are a few animals I picked out from the animal companion list: badgers, birds (some types of eagles eat fish and might be a good fit?), boar (of course), frogs, giant porcupine, reef snake, giant salamander, giant skunk, stags, as well as anything aquatic, though those are difficult to bring along on an adventure. I've kept it light on the predator side, so some kind of big cat would probably fit in well there.
Do we have an established latitude for Ancorato, one which we can relate to a latitude on Earth?
For example, if Ancorato is supposed to be similar to Hawai'i, then one could look at Hawai'ian wildlife for a guide. (Possibly prior to human settlement - humans have a tendency to hunt things to extinction.)
We don't have exact latitudes, but it states somewhere in the first book that it is sub-tropical climate. Descriptions of plants (oaks, evergreen, but also some palms and fruit trees bearing mango etc.) seem to fit with this: it's not the jungle, but it's quite warm. When picking animals, I've mostly gone at it based on what I would expect to survive on the beaches and in the forests in Florida.