If you can tell your tyre dealer exactly what sort of wheel and tyre you need, there's nothing against doing just that. However, the emphasis is on exact details. Apart from the obvious, this includes wheel rim offset, hole pitch diameter and number of holes and, very important, the tyre load rating. Tyre dealers used to selling car tyres often overlook the fact that caravan tyres are usually of a higher load rating than the equivalent car tyre, especially if not told that it's for a caravan.
Going to your franchised caravan dealer is normally the safer bet, though.