The fact that your girlfriend owns a home and you want to put her on your new mortgage, this can work, however you need to consider a few things.
If you do not sell her house first, this will count against you when the lender figures the DTI or Debt To Income. This ratio cannot be more than 28% on an FHA mortgage. So in other words, 28% of yours and your girl friends monthly gross income will be considered when qualifying you for a new mortgage. This 28% would be your maximum house payment including taxes and insurance.
So if you do not sell your girlfriend's home, then you can rent it hopefully for more than the payments are and this will help relieve the hardship.
The lender will take the lower of your credit scores. So if she has a lower score than you, it will only work if her score is above 580.
To make it worse, you will not be able to qualify for the first time home buyer tax credit if that is what you're thinking. One of the tax credit's requirements is you cannot be a home owner for the past 3 years. So then, since you're just now selling her house, that may knock out the tax credit idea.
This is not likely what you want to hear, but it's the cold hard truth.
Do not give up though, get her house sold, save money for a down payment and still buy a new home with an FHA mortgage. It really is the best mortgage product for first time home buyers and has been for decades.