Hi Greg,
If you are going to play motorsport then yes, a trailer is piece of mind. It also makes moving the car about the place without relying on others, for whatever reason, a much more straight forward task.
The main issue with a car trailer is storage. My last one (from Qld) spent most of its sleeping life in the street chained to a Sydney telegraph pole, however my current trailer (from Sydney) lives under cover in the shed
For Cobra's a beaver tail is best to facilitate loading. If you have fully covered deck then the trailer can do double duty carting other things around and whether it is up to the task.
Electric brakes are good, but then not so easy to swap tow cars......though perhaps this can be seen as a positive
Be mindful about what you are going to tow the trailer with as well.
3k should get you something preloved but you may need to be patient. Ebay usually has a number as does
MY105.
Cheers