I have sewn a little on leather and a little on fake fur. I think all you need is a machine that is pretty heavy duty, some heavy thread and a heavy duty needle. I remember that you can pull the fur out of the seams after you get them sewed together, with an implement like a needle or something long and thin that is not sharp.
I think you will probably want large seam allowances like 1/2" to 5/8", at least. I was thinking squares, but you could probably do strips, too.
I hope this helps, it sounds like it would be really pretty- and welcome to the board from western Washington State!