Ponies trained in eventing are expected to be able to demonstrate proficiency in dressage, show/arena jumping, and cross country (not held in an arena and the pony must jump "obstacles" as opposed to standard jumps). The requirement that the pony is competent in multiple disciplines helps keep things from getting boring.
Eventing is really fun but does require a fair amount of work on the part of both the pony and the trainer.
As with most discipline specific training, your pony should know the basics of ponyplay including rein aids, leg aids, and the various gaits. However, it is not necessary for the pony to know much dressage or have experience jumping since these can be learned as part of training for eventing.