I wrap my Hobb's 80/20 in a twin size sheet and put it under one side of my quilting frame. When I need it I get hold of one end of the sheet and pull it out and the keeping hold of the sheet roll the batting back under the frame until I have the length I need. cut it off, the roll it back up and under the frame it goes
About the dolly, you can get one a Wal-mart they sell the to go under their metal file cabinets. You can cut a piece of plywood to put on the dolly and maybe screw it to the frame and attach a length of closet dowel the set the roll of batting on.