Do you have a serger or access to one? I'd serge all around to prevent raveling then hand wash it delicately and throw in the dryer on delicate also. That's the only thing that will get rid of the hair and dander. Good luck.

We also have a cat that sheds non-stop. What I have found that works well is to get a pair of those yellow Playtex gloves used for washing dishes or cleaning the bathroom. Put them on your hands and then gently rub all over the quilt. It is amazing how the cat hair just rolls up and comes off. After you get all the cat hair off, then take it outside and give it a good shaking to get the dander out. This also works well for getting car hair off of the couch or out of the corners in a carpeted room.
Good luck!

Along the lines of what Anna said, a small zig-zag along the outer edges would help before putting in wash or dryer. I'd throw it in the dryer on low with a damp cloth.