I would have thought that in the UK it would be a requirement for LPG/gas refrigerators used in caravans to be type approved, and flame out detection is mandatory for these units. In order for the caravan containing the gas refrigerator to be properly registered it would also have to be inspected and certified by a qualified gas fitter, and he wouldn't allow certification if the refrigerator didn't comply.
In Australia the requirements for gas refrigerators in caravans would probably be similar to those in the UK and any work carried out must be by a qualified gas fitter. Assuming that your refrigerator does have flame outage detection then adding the appropriate components to provide a LED indicator should be fairly simple although carrying out the modification yourself might be frowned upon
Having said that the following document explains flame outage and what usually happens to cause this problem.