Perhaps what you and your mother can do is to execute a normal transaction --- she selling the property to you, and you going through a mortgage company.
Shop around for lenders and find the best rate. How about contacting the lender who currently holds the mortgage? They may be more motivated to service a new loan for the same property.
Here's a link to an article that explains quit claim deed. The situation described seems to parallel yours. http://www.thinkglink.com/Quit_Claim_Deed.htm
Apparently you were given the wrong advice when the property was quit claimed to you because lenders ( and this has been their outstanding policy) require that the property is in your name for one year( it's called seasoning ) and you have to prove that you are also making the monthly payment for that 12 months. Right now, is there another child that your Mom can sell this property to? This is really ot the best of situation.
Every lender has their own internal policy as to when and how you can refinance a property. Some require 12 months on title, some require a day. It probably would have been easier for you to buy it from her with a gift of equity but it's okay that you didn't. Flagstar allows one day of title seasoning in order for you to refinance the property. If you would like to contact me to discuss your options, I'll be glad to go through it with you. Usually in order to refinance, you just need to quit claim before the application is taken, which you have done. I don't think you should have to wait a year.
Please take the opportunity to call me at your nearest convenience.