To my knowledge there are NO hotel shuttles from LAX, but there is Supper Shuttle service. Orange county would be closer if you can go there instead.

As for the hotels, it may not matter too much, as you should be spending most of your time in the park instead of the hotel. However, if your daughter is young and you need to go to the hotel room during the day, you may want to consider one of the Disney properties on the Monorail line. And it will probably be hot and crowded.