Oh boy! I just did this ... on Wednesday last week!!!! You can certainly do it (Make sure you put soap in the washing machine, just water doesn't take the markings off). There could be two problems - one - the batting might shrink more than your fabric (that's what happened with mine) ... two - it can go really wonky, and then you have to block it to make your quilt square again.
From experience (mine was pretty funny LOL), I would baste with a brightly coloured thread the area that is not quilted (i.e. black on white) before you wash it. This way when you wash it, if there is any shrinking of batting, it is minimized because you have sewn most of it down. And when you go to take the thread out, it's easy to see.
Also, I wouldn't put it in the dryer to dry, I'd let it dry on it's own ... you could block it that way to, so you wouldn't have to do it again. If you look in this form (MAIN) and look for my thread wholecloth - need ideas, you will see what I went through and the advice I got.
Good Luck!