Certainly the "Track" will handle a "conventional" caravan :)
Whether the caravan will handle the Track depends mostly on how it is driven.
Unless it is wet (in which case give it a miss in any vehicle), the Oodnadatta Track is navigable with most vehicles, with care and attention and at "moderate" or slower speeds at any time.
The Oodnadatta Track is possibly the most interesting of all of Australia's iconic "tracks". Take your time and enjoy it to the full.