While different countries have different rules on how old you must be to trade shares or own real estate, it's usually legal for to invest in gold from any age, whether as coins, bars, jewellery or – for better security and lower costs – as physical gold bullion held and insured inside specialist vaults.
Using BullionVault, children under 18 can open an account to buy gold, silver, platinum or palladium, so long as their legal guardian also provides I.D. documentation and helps manage things until the child is old enough to take control.