It's difficult to find a entirely satisfactory answer. You will have to do a bit of your own investigation.
Consistently battery related web sites will tell you that AGM batteries require a long slow charge, and that keeping them on continuous charge for long periods to keep them topped up time will damage the batteries performance and shorten its life. AGM batteries also work best where the discharge rate is also kept relatively low, which is why they are not often used to start cars, becasue heavy engine starters can draw several hundred Amps during cranking, and AGM's are not good with high currents.
Normal caravan habitation duties should be fine, but you should the battery is designed to cope with the peak current load current (Stalled load) of your caravan mover.
They also mention but do not detail the need for a differnt type of charger.
I cannot tell you if which if any caravan charger systems are compatible with AGM batteries. You will have to check teh specifications of the unit you have fitted. If it does not have specific instructions for using AGM batteries, then it is safest to assume it is not compatible.
You need to check the chargers manufacturer if an AGM compatible replacement is available for your model.
You then also need to know the charging specifications for the model of battery you are intending to get, and to make sure its compatible with the charger.