I have an off-brand replacement battery for a five (or six?) year old Dell laptop that has worked just fine for me for the past two years. I think I picked it up from either Amazon or NewEgg.

You would be fine with either ordering a replacement from Dell, or going with a replacement from other sources. Usually, you'll pay more to get one from the manufacturer, but some people find a little peace of mind from that. Doing a search on your model name/number should turn up numerous sources for price comparisons.