Quit Claim Deed

i had just bought a house 2 months ago and was getting ready to move into it. but just recently i found a bigger house which i fell in love with and planning on buying it. i had leased my current house to the lady that was already living there with her kids for the mortgage payment. the lady offered to buy my house but wants a quit claim deed adding her name so she can refinance it for lower interest . is that possible to do ??? or what should i do ?? is it possible to do novation here ? in other words what is the easiest but safest way for me to sell her the house - she likes it but dont have enough to put down & closing costs.
last question-would being a owner of this house prevent me from buying a second house & keep leasing this ??

thank you