Sounds like a great idea - I've paddled most of the canals around Doncaster - although I wouldn't paddle on the Don - it's tidal and pretty filthy down river from Doncaster.
I can recommend the Stainforth - Keadby canal, it cuts through some very pleasant countryside and there aren't many locks getting in the way. The "New Junction" section between Stainforth and the Aire & Calder is also really pleasant, quiet and I think just the one lock. Aire & Calder on the whole between Goole and Knottingley is ideal, but gets a bit industrial after.
I'd give it a go, there are plenty of quiet spots to camp - let us know how you get on.