Any fabrics that don't "fray" without a hem?

I make clothing for my dog, don't even own a sewing machine yet so I've been doing it by hand. Never anything fancy, just "4 legged" outfits to keep her warm. So far I've made about 5 out of fleece simply by cutting the pattern and sewing the pieces together and they're excellent, very durable and have lasted a while. But fleece is the only fabric I've gotten that I don't have to "hem" the edges to keep it from fraying. Are there any other recommendations of fabrics that don't? It would take me twice as long to go over them, so while I know it's possible I'm trying to avoid that now. Fray Block hasn't helped much. Obviously once I get my machine I won't care but I'd like something meanwhile, and wondered if there was any other fabric like fleece that doesn't come apart at the ends. Thanks!