Bigger battery will not make it go faster, it would only give you longer running time unless the old battery is completely nackered. A higher A/h battery would give you a longer run time and should be available in any good electrical wholesaler
I have seen videos of people buying things like these off of Amazon and then sticking a dewalt or equivalent battery into it. Serious power judging by the videos. Just make sure the kid is wearing a helmet. They look to have serious torque.