Hi Tram,
Much as Lisa says,
A hair dryer will typically use 1to 1.5Kw. Such large inverters are quite expensive and to meet such power requirements it will impose a current draw of between 80 and 120A on the battery.
That rate of discharge will damage most leisure batteries, and of course flatten them very quickly in a mater of Mins. So such inverters in a caravan are not a practical choice.
Car batteries may withstand the rate of discharge better, but these tend to be have less charge capacity so will flatten even quicker.
The use of such a device in car would need the engine to be running, and the inverter must be located close to the vehicle battery to minimise voltage drops and to keep the cost of the copper wire down.
Over all the use of such large inverters is not a practical proposition for a caravan.
Best advice - either use sites with EHU's or consider divorce.