Yes you probably can qualify, but I would strongly suggest contacting a good mortgage person before doing anything.......including paying anything off. Also, the credit report that a mortgage person sees is going to be different than what you can obtain.
Many houses qualify for FHA loans with only 3.5% downpayment, but in smaller towns and in rural areas, you can get a USDA loan for $0 down. VA loans are $0 down also.
I can be reached at 816-419-6508.