More thanks to Factobrunt for his observations on the Pig Sty Camera Question.
He's got the clincher, too, with his remarks about ISO. An SLR can have a relatively high ISO, which means I can take pics in poor(ish) light with no flash. I want to be able to do that to take relatively unobtrusive pictures, like this one.
Now the only question is which DSLR? The Canon EOS 350 is used by a lot of people on Flickr, including my mate Sam. There's a new Olympus out in the same price range.
Speaking of price, as we've a new baby and I've got a part time job, I can't dash out and buy something this expensive just now. So for the first time since childhood I'm Saving Up. No need for snap decisions, therefore, and a bit of fun making the decision meanwhile.