Hello Eddie,
As John Watson says, the majority of caravan heaters (Carver, Electrolux and Truma) are safe to use because they are 'Room sealed'
'Room sealed' heaters are designed in such a way to totally separate the burner, heat exchanger and flue gasses from the air inside the caravan. All you get inside the caravan is clean hot air.
As with all gas appliances it is important that they are regularly maintained and checked by a competent gas fitter.
Such heaters are as safe to use during the night as during the day.
If you believe there are fumes escaping from the heater then the heater must not be used at all until it has been checked and if necessary repaired. In most cases where 'fumes' are suspected, it turns out to be dust/hairs on the heat exchanger.
It is my experience that the 'room sealed' feature is usually quite robust, and is only likely to be compromised if someone has tampered with the appliance or it has been damaged.
Obviously the choice is yours, but unless the heater is not room sealed or has been damaged, then it is a perfectly safe appliance to use all night.
You actually get far more fumes from your gas cooker and