If she can come up with that much loot to put down then she can get a loan for the whole thing if she didnt have shady credit issues or something else going on.
I voted hell no. Ive seen too many cases of missed payments, accidents, parking tickets and more.
Whos going to make SURE its insured? Are you going to insure it for her and make her pay those premiums? You DEFINITELY CAN NOT trust someone to pick up insurance on YOUR vehicle these days.