The only pony racing I'm aware of is at some steeplechase meets they have pony races on the flat before the main over fences races.
I know that the Essex Hunt used to have pony races at the Far Hills Race Meeting at Moorland Farms, you might try looking into that.
You might also see if there are any other steeplechase meets that offer pony racing. Check the Chronicle of the Horse website under steeplechasing, that may get you started in the right direction.
If your daughter is serious about this, the pony needs to be conditioned like a racehorse, which means galloping 1 - 1 1/2 miles 6 days a week a minimum of 60 days before the race, 90 is better. I'll also warn you that the pony races at steeplechase meets are pretty competitive, especially the large pony division. It's dominated by steeplechase trainer's and rider's children, who have conditioned their ponies alongside the racehorses. And sometimes the "ponies" are TB racehorses that happen to fall under the height limit.
I hope someone else on the board will have more info.