In order to be in full compliance with Ohio law, an elder will need to confiscate the said firearm upon your arrival at Millers. Then you will be bound and your eyelids held open (think Alex in Clockwork Orange) whilst a group of elders examines your device, test fire it (I'm thinking 5,000 rounds, just to make sure) for safety, and then pronounce it suitable for so one so tender of age. However, you must then clean the guns of everyone on the line, to demonstrate your skills in this area, before you are allowed to shoot your pistol.
More seriously, from the same source you qouted:
JUVENILE SALE
Is it illegal to sell guns to kids? Yes
State law restricts selling or giving handguns to juveniles under 21, and other firearms to juveniles under 18, except for supervised loans of firearms or for limited lawful activities (such as hunting).
So technically, this is your parent's pistol until you turn 21. Make sure the officer understands that.