It is a LOOOONG way from LAX to
Disneyland, believe me. If we are going to the Disney area, Anaheim, we NEVER fly into LAX if we can help it. If we are going to Anaheim we fly in and out of John Wayne airport, about 5 minutes from Disneyland.
If you fly into LAX, it is at least and hour, if the traffic is NOT normal, then it is expensive to stay at the resorts hotels, and then y9u would have the hour (at least) drive back to the port the next day. If you were going to do several days in Anaheim it might be worthwhile, but not for overnight.
Ships out of Los Angeles come and go from docks nearest to Long Beach, though most of the cruise ships do their transfers from LAX. Not enough people could ever come and go from Long Beach to make it financially viable to provide transfers.
So what I would do, especially if I could book on Jet Blue, my personal favorite, would be to use Long Beach. Arrive the day before, if possible, and take a cab to a nearby hotel.....there are many. And then a town car or taxi could be hired, pre-arranged, to take you to port.
From experience, I HAte LAX and would do anything not to fly there.
Marilee