Can I quitclaim deed my property over to my mother if I have not paid off the house? If so, can she simply take over the payments? How will this show on her credit and my credit report? If she is ever late, who is in default with a quitclaim deed?

Please respond??

No , not really.

If you have a mortgage on the property, you may be able to add her to the deed but not "sell" her the property. Any transfer is like selling.

Next she can not just take over the mortgage unless it is set up that away, and they allow her to, Most likely she will need a new loan, pay off the old loan, and then transfer the ownership over by deed.