How can i convince my trainer that i am ready to start helping her train ponies?

She will tell you when you're ready, not the other way around. I don't want to be nasty but if you want to play with a horse, find a well broke adult horse to play with. Sure, youngsters are cute and fluffy and your new best friend, but when they want to be they are also biting, kicking, rearing, dangerous wild animals. And they need expert handling. If you get it wrong you can wreck them for life, or put yourself at risk.