What can make a dragon familiar suitable for a low-level character?

I would like to allow a level ~5 character to have a dragon as a familiar. (My DM style is a little more flexible.) Other than having a “baby dragon,” how would you keep that balanced? I’d also appreciate any advice about running a dragon-assisted campaign.

Addendum: What if I just reduced the HD, and restricted a few abilities? Example, too young to fly, but intelligent to talk and give additional reasoning. Randomly remove a spell-like ability, and/or supernatural ability.

Would I be restricting the player too much, by actually turning the dragon into a pet she needs to take care of, rather than an independent familiar?