Is sleep time the only time she's pulling off her diaper? If not, then I would question whether the diaper is bothering her in some way.
Other than that, all I can suggest is that you might try to introduce potty training and see if she seems ready. If, after a couple of days, she obviously isn't, just tell her it's ok and that you'll try it again later...
As for the problem of laundry.... unless she moves around a lot in her sleep... you may be able to make up a smaller waterproof pad system to put under her, so that all you have to launder is a small sheet or blanket and her bedclothes each time. A towel over a large piece of plastic material might even work...
My guess is that this is a pretty temporary problem. I know it's frustrating for you now, but if you can keep in perspective that it's not going to be forever, that may help you get through it.