I would forget the trailer. There are a few access points that you can pre-stash water at. If you are starting on East end (Loma) the first place would be Rabbit Valley, then Westwater, Cisco, Dewey Bridge and up Onion Creek, all are accessible by vehicle. You should be able to carry enough water to make each point.
About 15 years ago I was a member of the Grand Valley Mountainbike Patrol where we patrolled the Loma side of the kokopelli Trail. I once came across a guy (who was from Germany) who was going to do the whole Kokopelli Trail by himself and during the summer to boot. He had a 1 gallon jug of water with him. I told him that he was not going to have enough water to make it and what his plans were to get more water along the way. He told me he was going to bum water from people with motorhomes that were camping along the way, I told him his plan was pretty weak and that the chances of coming across someone was slim. He didn't want to hear that and was determined to do it anyway no matter what. After a few more tries to convince him to reconsider he took off. I let the BLM know about this guy and what he was going to do, never did hear anymore about it.
Ive done this trail twice. First thing - a trailer is totally out of the question. There is some severe hike-a-bike, and you would have to disconnect the trailer and make two trips if you were doing that.
I did it on a Salsa El Mariachi with frame bags both times. First time, I did it with car support, my wife met me at Dewey Bridge with the car for camping one night there. The other time we did it unsupported - camping near the boat launch one night, and up past Fisher Towers the next night. Water is a challenge. On the unsupported one, we took an MSR ceramic filter with, but it clogs up easily with the silt in the river. Best thing is to take a large water bag and some alum - bag the water out of the river, sprinkle alum to help it settle, and then filter out of the bag.
I would recommend you get yourself a nice steel hardtail, frame bags, seat bags, and bar harness from Revelate, a nice water filtration system, and get your total shelter/clothes/food/tools/spares system down to 15lbs or less, and hit it!
Your first concern, water, isn't as much of a concern because the trail itself follows the course of the Colorado. It does climb above and consequently fall back down to the river. Bring a couple of dromedary bags that you can fill and and sling if you plan on dry camping.