I'm confused what you mean by qualified for FAFSA. FAFSA is the form you fill out to determine your family's expected contribution (often referred to as your EFC for shorthand) it is not a form of financial aid in and of itself.
Is your EFC 9K? (Meaning you're expected to be able to afford up to 9K per year towards costs)
or...
Is 9K what's left after you subtract expenses from your EFC? (For example, if total estimated costs per year are 40K at the college of you kid's choice and your EFC is 31K, then you qualify for 9K in financial aid.)
The best route for borrowing are government-backed Stafford loans, take the max of subsidized (if you qualify, you have to be lower income) and then take unsubsidized ones. Unfortunately the other type of gov't backed loan, the Perkins loan, looks like it was recently discontinued by Congress. Stafford loans have better interest rates, are easier to defer or put into forbearance. They can also be consolidated after graduation so you can lock a good interest rate for the life of the loan if the T bill is low. (* note that it seems like Stafford loans are now called Direct Federal loans, though a quick google is a little confusing)
After maxing the Stafford loans, you probably have to go to a private loan and in this case I'd advise you to just shop around as you would for any loan for the best deal on terms and interest. Beware that private student loan debt is just about the worst kind of debt to have outside of being indebted to a loan shark with hit men.
Like others, I would insist on giving up a car, take a work-study or part-time job and/or any other frugal means before maxing a loan. It sets up much better financial habits and won't follow you around like a ball and chain after graduation.
Also second the recommendation to talk to the school. Every school has financial aid professionals and college admissions professionals who can help you navigate this. (Small disclaimer: I was a college admissions counselor in the 90s before switching careers, hopefully none of this info is too out of date or incorrect, which I why I strongly recommend you to talk to one if you don't have a better resource than us here at MMM.)