Is Momo a dog, a rabbit, or what? She looks more like a rabbit than anything — although even then, her ears are a bit weird for it — but she's from a clan that, in other games, has included two dogs and a fox.
Technically (per Word Of Capcom in the BoF III and Breath Of Fire Complete Works artbooks), she is supposed to be a Grassrunner (dog/canine people)...but her subclan had to have been particularly long-eared. And no, you aren't the only one to think "BUNNEH GEEK GIRL" seeing her for the first time—this troper wasn't sure until reading the info in the artbooks...
They're not bunny ears. Take a look at her ears, then look at Scias' ears (in Breath of Fire IV). Not quite identical, but more similar than not. She just falls under the Bizarre Sexual Dimorphism / Cute Monster Girl trope and so looks less obviously doglike.
On close inspection, her ears resemble that of a Papillon breed dog.
This troper always thought she was wearing two feathers on her hat for some reason...
Are the rights to the series in legal limbo? No PSN re-release or sequel in a decade now and no Breath of Fire characters in Capcom vs. Whatever.
Fairly recent moves by Capcom (licensing of the manga adaptation and (finally) re-release of Bo F IV on the Playstation Network) do show that the rights aren't in as much legal limbo as thought. This includes level-up cards in the "Heroes and Heralds" mode for Ryu (from the original Breath of Fire), Nina (from  II), Fou-lu (from  IV) and Lin (from Dragon Quarter) in the upcoming Ultimate Marvel Vs. Capcom 3 which pretty much settles the question for the licensing (re the one game in the series where there may have been licensing issues).
In addition—there has been some fairly recent discussion of  finally ending up in a Capcom vs. Whatever (in some method other than a "card game cameo"); according to a developer blog for Marvel vs. Capcom 3, they really wanted to put Fou-lu in but decided not to at the last minute due to the Mv C series being heavily geared towards US audiences. If a  character ends up properly in a Capcom vs. Whatever, it's probably going to be in a "versus" game that would be popular in Japan (for example, Tatsunoko vs. Capcom)—especially since the same developer blog, they still want to eventually stick a certain god-emperor in a Capcom vs. Whatever at some point.