Don't forget, initially a DSLR can be used as a point and shoot if set to fully automatic on the dial/menu. My guess is that it wouldn't be that long before you would like to be able to "manage" the types of photos you can take. Having started out with a compact camera like many do, one soon comes to realise just how limited they actually are in many situations.
Compacts as have been already mentioned are great at what they do, there is no doubt about that, but what you should take into account when deciding is how far into photography you want to go, its a very catching hobby . As always research -research and and once more, try out a couple of cameras inshop before purchase and weigh up the pros and cons of each.

Bazza