Hello Phil,
A large proportion of new caravans are fitted with electric heaters, and many have a 2kW setting, so it is quite likely that you will be able to use a 2kW fan heater. A 2kW heater will use 8.6A of current. Most heaters have a lower power setting, which will use less current.
You must however be aware that the mains hook is limited in the amount of current that you can use. Whilst your caravan will be wired to accept 16A, the sites wiring may be rated to a lower figure. In the UK it is usually between 10 and 16A, but elsewhere it can be as low as 6 or even only 3A. Your site operator will be able to tell you of the available current.
You must also allow for the current that other mains appliances will use in the caravan, a fridge will typically use about 0.5A, a water heater about 4A, a television up to 0.5A. It may be the occasional items that might trip the supply such as a kettle, or a microwave, when they are used at the same time as your heater.
With a little forethought and care it is possible keep the current consumption under control, and no problems, but if you try to use more current than the site allows you will probably trip the sites circuit breaker.