From what I gather, you seem to like books which talk about people who have a bond with one special animal - at least, that's been the case with the Heralds novels by Lackey and the dragonriders of pern by McCaffrey. I used to like this kind of stuff myself
So I thought maybe you'd like Chronicles of the Cheysuli by Jennifer Roberson. The first volume is titled is The Shapechanger's Song and features both people - the Cheysuli - linked to animals - wolves, hawks and others, it depends on the character,
and a strong female protagonist, at least in the first volume, that is, Alia. BTW, the Cheysuli can as well shapechange into the form of their lirs - that is, the animals they are linked to.
Besides, I'd recommend as well reading the Darkover series by Marion Zimmer Bradley - Stormqueen! or Hawkmistress! for example ( I prefer by far The Heritage of Hastur/Sharra's Exile, but the two I've mentioned before have strong female characters)
And, as a long shot, I'd propose the novels protagonised by animals, as ie. Tad Williams' debut novel, The Tailchaser's Song, a fantasy book about cats, or Duncton's Wood by Harwood - about the moles.
As for Pierce Anthony - depends what you've read: his comic fantasy (Xanth) or other books, like The Blue Adept? You could try to find other books by him - he's really written a lot!
Hope this helps a bit