It won’t help your credit a bit
Paying off a car loan does nothing extra to your credit. In fact, on the long run it might even harm it.
What build and improve your credit is a stream of on-time payments. It will take you at least 24 months of on-time payment to re-build a reasonable credit score after the bankruptcy, and years to build good score.
If you prepay car loan (or any other installment loan) you stop making on-time payment. While this in itself doesn’t hurt your credit, it doesn’t help it either because it stops building it.
What I’d suggest is to keep making payments on that car for the next year. That will improve your score, but I doubt if it will be enough to qualify for a new car loan after a bankruptcy. Credit scores are just a small part of any lending decision. What’s on your credit report counts much more, and a bankruptcy something any potential lender doesn’t like to see. Other factors such as your debt-to-income ratio and employment stability also have big impact on any potential creditor’s lending decision.
To improve you credit score and debt-to-income ratio prior to applying for a new car loan, I’d like to recommend on this technique. It will certainly improve your chances of approval and get you better terms.
Good luck.