It depends what kind of trailer you have. We took our offroad camper up that way but set up our base at the King Edward River campground (there are two options - we stayed the campground to the left, can't remember the name). It's much nicer than the Mitchell Falls campground and has a great waterfall and swimming area of it's own. It was one of our favourite camps in the whole of the Kimberley. There's lots of great Wandjina and Bradshaw rock art nearby too.
It took us just over an hour to get to the Mitchell Falls carpark from memory, but the road had only just been graded and opened up and was in fantastic condition. We also didn't come across much traffic and weren't towing. We did do a tyre on the 4wd on the way back from Mitchell Falls though. There are lots of large-ish rocks that line the edges of the road (where the grader pushes them), so just take it easy.
We did have a shock come loose on the Kalumburu Road (it had been punished though on the back road from Cape Leveque and throughout the rest of the Kimberley), but we just took it off and replaced it when we got back to Kununurra... no dramas. Drysdale Station can fix it if need be.
If you're worried about your trailer and you have a tent with you, leave the trailer in the Drysdale Station campground.
One other thing to be aware of...we filled up at Drysdale before heading up to the falls for a few days and had planned to fill up again on the way back down, but when we came back to Drysdale to re-fuel, the fuel truck had broken down on the Gibb River Road so Drysdale were rationing fuel...30L/car
We luckily had a jerry can and topped up enough to literally roll into Home Valley on fumes.
The Mitchell Falls are absolutely spectacular. Breathtaking even. I can't wait to go back
It's a magic place over there. Enjoy your travels
Karen