We did the Dumbo Dash the first time this last trip with our 3 yo DD. We were at the entrance about 20 minutes before opening. After the RR/opening show, walk briskly to and through Cindy's castle. There will be another rope there with about 50-100 people. When that rope drops, head right for Dumbo. You will probably be on the first or second ride. People are right, the wait for Dumbo is "Short" for the first hour or so, but "short" is 15-20 minutes, and to me, any time wasted on this ride that is the most pedestrian and the shortest (maybe 90 seconds) ride in the park is too long, but in the end it is a classic, and a MUST-DO if you have little kids. We were off this ride by 9:05 (park opened at 9 AM) and able to enjoy the rest of fantasyland. We went to Cindy's carosel next with no line, and by the time we were off that, there were at least 100 people in line for Dumbo. We then walked on Pooh, Peter Pan, and Small World, so doing Dumbo 1st does not hurt your chances on the other FantasyL rides.
Other posters..please don't flame me for calling Dumbo pedestrian...I just mean that for how unique and magical most Disney rides are, of all of them Dumbo most reminds me of a "county fair" ride. That being said, we rode it both times we visited as a couple, no kids, but would never wait more than 30 minutes.
OK, flame on!
SkierPete