Pretty much agree with Samaath. A key question would be where the right to restrict comes from. It can be in the CC&R's where it may explicitly say how many pets and what kinds...in an HOA I know about, it says 2 domestic animals of a common nature in the CC&Rs for example. If it's in the CC&Rs getting it changed is likely to be a huge challenge.
Or the CC&R's may give the Association (usually the Board) the right to regulate house pets. In that case you have to convince the board to change the regulation to allow this breed; and you may find that difficult or easy, or may have to convince a lot of other residents to agree to support your request.
Finally, and this is one you should check, it may be that there is no right for the association to make such a restriction. The CC&R's say what the basic powers of the association are. My CC&Rs say that the Board can adopt rules to govern the use of the common parts of the association. It does not have any authority to regulate domestic pets as long as they are not a nuisance -- making noise, creating unsightly conditions, smells, etc. They could say people can't walk their dogs on common grounds, for example, you'd have to transport the dog in a car to the park.
If they don't have that authority then the regulation is not effective.
I say the last because it is not all that unusual for an association to attempt to exceed its proper powers to regulate. So you should check it all out and see where the regulations come from and what makes them binding. I've had my HOA withdraw a bunch of "rules" they "passed" that they didn't have any authority to do, and helped them to create some rules that they do have.