Hi Lisa,Look at PetsMart Charities, Petco Foundation, the AmericanHumane grants family. I'm assuming that your breed group has not received grant funding before? If you work with any other rescues, or other nonprofit organizations locally (or even, nationally), be sure and ask them if they know of potential funding sources you could contact.
Does the AKC have any funding for breed-specific groups like yours? I'm with a cat rescue, which is not breed-specific so my funding world is a little different. Oh, you can also see whether some of the larger food companies are interested in offering assistance.
One warning: I think (I'm not a grants professional as are many on this group) that winning funding for a shelter's construction, for a "capital" project, may be a tough sell as a first project funded through grants. You and your board might want to explore whether there are some smaller funding needs that you could approach funders for help with, to sort of show your track record is good over time. If the shelter could be multi-use, you might be able to collaborate with other organizations that would use it, and that might strengthen your application if the other orgs are well-known to the funders.
Good Luck!!!