The one thing you definitely want your child to emulate about their heroes is all the gear they wear. Helmet, chest protection, boots, knee braces, gloves and goggles are necessary investments to your child's dirt bike riding adventures.
Approach dirt bike riding gear for your child the same way you approached buying the bike with the exception of buying used. We'd recommend new gear unless you're comfortable using a hand-me-down from a family member or close friend who you trust. Even a small crash can damage and impair the quality of gear - especially a helmet.