My wizard wants a pet dragon

And I want to make it happen. I am just unsure on how to do it.

I was considering cooking up a special version of find familiar - though the dragon being unable to attack would surely take away from what my wizard wants his dragon to do. The whole fantasy is of course to have a little snapping drake at your feet while you fight.

Then I considered just making it an animal companion - but it also is quite the strong companion! Especially if he wants it to grow up! So here I am worried about him very quickly outclassing his fellow companions. As a bladesinging wizard, the least thing he needs is to pack more of a punch in combat.

I also thought about offering him a dip into drakewarden ranger, because essentially, it does feel like that is what he is asking for. But I don't know enough about multiclassing to get a good sense of how much that would cripple his character in the long run. Generally though the campaign does not require a min maxed character and we have other party members who dipped into other classes for flavour only.

Am I missing something? Is there a good way to make this happen without giving my wizard too much of a leg up on his party or punishing him too hard for wanting a cute pet? Any advice is appreciated!