As per Maria Luisa...
A blue jacket wouldn't be right for showing M&Ms unless it is a tweed where blue is just the predominate colour. The colour really depends on the colour of your pony. We go for mainly brown on our palomino (see photo) and a sort of dark creamy colour with big pale blue checks on the grey. They should have plain plastic buttons - or those with foxes heads. Plain blue jackets are for show ponies and no gold buttons.
Definitely nothing black. Numnah, boots, whip etc should all be brown. Like Maria Luisa we use Fylde saddles and bridles. We have had their numnahs and they are great but we've changed to Courtlea now. Girths should be brown or white.
Most keen show people will buy a Charles Owen (or similar hat) for showing which has the velvet as part of the hat with a subtle flesh chin strap. We have blue to go with the grey's outfit and brown to go with the Brown jacket.
If you've got a crash hat that is fine to start with but I'd recommend a blue velvet cover rather than black which a definite no.
For the Palomino which does just M&M FRs we don't trim him at this time of year - he has a chest and tummy clip in the Winter - except we keep his ears and chin neat. We don't do his tail but would do if it was dragging. However we wouldn't bang it - we'd shorten it a bit but keeping it natural.
The bridle should be brown and simple. Just a regular noseband without flash (don't even have a flash attachment on it) and a snaffle bit. In FRs some children use a Wilkie but if your pony goes well enough without it then you'll be better thought of by the judge. We have plaited brown bands now because they are the current fashion but plain ones are fine. Definitely no velvet on an M&M browband!
Cream jods are fine but more yellow ones are popular. Definitely no half chaps and make sure the jods are held down by elastic or clips.
For leading you need to get a leather lead rein which attaches to the noseband - not the bit. Obviously you'll need to kit yourself out as well. Nothing fancy - should be sombre colours with probably a hat which matches the jacket. You can wear shoes or "Dubarry style" boots these days.
Get Horse and Hound - it'll have lots of photos to get you going or look at photographers sites who cover the shows such as Equinational etc they will have dozens of photos for your to copy.
Most of all I'm pleased that your DD is having fun and wants to give it a go!