You know your child best. Are they eager to get out the door and ready with helmet and boots, or do you have to remind them that it's time to leave and be properly dressed for their lesson? Observe your child during lessons. Are they attentive and enthusiastic, or does their attention wander? Do they brush the instructor off and answer every instruction with 'I know', or do they try to apply what they are being told?
Do they get off the pony and hand it to the instructor, or are they excited about unsaddling the pony and putting it in its stall. Are they enthusiastic about being invited to equipment and stall cleaning sessions, or do they avoid any extra work?
If your child shows enthusiasm for all aspects of riding and pony care after several months of lessons it might be time for their own pony.