Yes, you can brush out loose hair and use that, too. It may just take a bit longer to get enough to work with. Learning to spin with a drop spindle isn't hard, is there a spinners/weavers guild anywhere in your area? Check with 4H groups, the local agricultural society, the folks that run the county fair, or try the SCA ( sca.org to find a local group), they often have members that do fiber stuff.
Sending it somewhere would be more expensive, and the mills around here have a minimum amount of fiber you have to send - I think one was five pounds minimum for turning it into yarn. Besides, working with your own fiber is fun!