Really depends on the camper. How you load the camper, axle position and drawbar length are all major factors.
Take a reading of your ball weight when the camper is fully loaded before you do anything. If its more than about 10% of the total weight of the camper then you could consider moving the spare. Be careful though as the amount of weight that moving the spare to the back takes off the drawbar is not a simple equation as other factors come into play.
As has already been mentioned you also need to consider the strength of the rear of your trailer and tailgate to support the weight.
In saying all that I have a 2007 Complete Campsite and I have moved my spare to the tailgate as the weigth distrubution was terrible. Which is probably why the new complete campsites have the spare mounted on the tailgate from factory