Diasterpiece has covered pretty much what I'd say - especially about not taking your own dpony if it could in any way spoil DD's day (we've had stable mates getting clingy and calling to each other before now which is a nightmare).
As regards classes best to check what it says in the rules. Certainly in affiliated showing it would be no problem riding in both LR and FR as long as child is correct age and pony correct height.
Obviously in LR then you'll need to have appropriate gear as well, including hat and long skirt/culottes and carry a show cane. You'll need to lead using a leather lead rope and basically you are there for show - hopefully at her age DD will be able to ride effectively herself. Remember though that LR are usually for younger children (DD rode in the from 2 1/2 to 6 1/2) and if she is big this could count against her in the overall "picture".
In FR she will be expected to ride around together at walk and trot - probably including a change of rein - and hopefully on the bit.
She will then have to do an individual show which should include trot on both reins and canter on both reins - no gallop! Best to make sure she has practised her show at home enough times that she doesn't have to worry about it on the day.
As regards Dartmoor just whatever you have should be OK. Ideally the saddle should be brown and you'd have a brown (fabric is fine) girth and definitely plain brown bridle. You could ride him in a snaffle or a wilkie - whichever he goes best in. I would suggest a plain brown fitted numnah - definitely not an oblong shaped one.
DD should wear tweed jacket, cream/yellow jods, jod boots (with clips if no elastic on jods), helmet with blue or brown cover (Charles Owens show hats with beige chin straps and felt are a good investment if taking it seriously in the future).
She should carry a plain and simple brown whip.
Good luck and let us know how you get on!