i toss my quilts into my washing machine then into the dryer all the time---if the quilt is too big for my washer (thick king) i take it to the laundry mat & use a big washer- but my queens wash up just fine.
you should never hang a wet quilt- the weight of the quilt can cause the threads/quilting to break- if you do not want to dry your quilt in the dryer it is recommended to lay them flat- in the summer time i take a king sized sheet outside & lay it out, then place my wet quilt on top of the sheet, then place a second sheet over the top (to protect it from birds/critters)...they dry quite nicely this way- you may need to turn it over at some point. I've also spread them out across my large hammock & again covered with a sheet to protect from birds....but most of the time i simply toss them into the dryer...i make them to last & hold up to use so expect them to be wash/dryable. even my wool quilts are washed & dried.