A female hare is called a " doe"

I think Jura is right: Hare is a fast animal that resembles a rabbit. There is no conjunction to hair. Of course doe refers also to other female animals. "doe" or "female hare"

I so want to say "haress". XD

I think you should say "doe-hair" because doe means not only feminine of hair but also of a deer, rabbit, goat, rat, mouse, ferret, and kangaroo.