The "spirit" definition is fairly obscure. I'd never heard it before. (That use of the word is apparently regional, FWIW.) It sounds like you originally started calling her "Gimpy" because of the way that she walked, which does make me think that you initially intended it in the more common sense of the word. You can name her whatever you want to, of course, but some people may not be amused. I do think it's a bit insensitive to poke fun at those with physical disabilities. While your family and friends know that you're being affectionate and silly, strangers might think you're being mean.
I don't think that someone has to be looking for offense to look askance at a pejorative term (even a mild one). I guess I see "gimpy" the way I see referring to a person as "Oriental" or "colored." While it isn't a slur, it's not particularly enlightened/respectful, either. In many cases, whether or not the term is offensive varies by region. I think in this case, it depends whether ableism is recognized as a form of discrimination or not. (In my neck of the woods, it's okay to refer to yourself as gimpy but frowned upon to use the word to describe others.)
You can absolutely name your dog whatever you want, but I'd be careful with this one. Imagine needing to call her at the park and realizing that someone with an injury or disability thought you were yelling at them (or everyone else thought you were). Yikes.