I dress lots of deer and antelopes (9 this year between the wife and me) and I think maybe the answers so far are a little on the short side, I think it takes more than 5 min to dress a rabbit. I don't time myself, but I think 15 minutes is closer to what it takes to do a nice job. I have a tiny little Gerber saw so I do split the pelvis and sternum. I used to do this with a knife but that is kind of a dangerous thing to do.
I start by skinning the udder or (censored word) off. Then I try to get the anus cut loose. Then I cut the muscle down to the pelvis with the knife, and then split the pelvis with the saw. Back to the knife to open the abdomen up to the sternum, and cut the muscle down the centerline of the sternum. Slip a couple of fingers between the viscera and the wall of the abdomen, and put just the very tip of your knife between them to open the wall up. This will usually keep you from cutting the guts. After you have the abdomen opened and the muscle cut over the sternum, cut it with the saw. Then back to the knife to cut the neck up the centerline to about the laranx. Then cut through the windpipe and trachea, and grab them and start pulling them down towards the butt, working things loose with your knife. You will have quite a bit of cutting to do around the heart, and then most of the diaphram will have to be cut. I do this by cutting it on the top side of the critter, then rolling it over and cutting it loose on that side. Then you should be able to just roll everything out over the hind legs. You will probably have to do some more work around the anus, it's hard to get it on the first try.
I take pride in having a nice job when I finish and the only blood is on my hands and tools and usually these can be cleaned up on the site. You will get better with practice, but I don't see any purpose in making a race out of it, the hunt is over, take your time and study how the critter is put together. I don't know why it is, but lots guys get more worked up dressing out a critter, huffing and puffing with blood and guts flying everywhere than they do while hunting.