I'm not understanding the reasoning here. In your original post you state:
I am going to pay off her 80k mortgage
This tells me you have $80K in cash right now. Why do the house need to be deeded to you? Just pay it off. There's a few issues with your plan that may or may not come back to bite your daughter.
First off, deeding the house to you, does not change the fact that she still has the mortgage. But in doing that I'm pretty sure that would put your daughter in violation of the current mortgage loan terms. That house is your daughter's collateral on your daughter's current mortgage. When they lender finds out she has quit claimed it (and they will pretty quickly too) that puts her in breach of her mortgage contract. The bank can (and most likely will) foreclose on the house if it's not immediately paid off in full, along with the penalties they can (and will) assess for breach of contract. So if it's deeded to you, add another thousand at least, to the payoff amount. That penalty does not add to the cost basis of the property either. It's a penalty, not a property improvement cost.
So why bother deeding anything if the intent is to just pay it off? The quit-claim does not make the mortgage go away. Only paying off the mortgage can do that. If you want your $80K plus what you invested in property improvements back, you can get that back when the property sells.
Since your daughter lived in the house as her primary residence for at least 2 of the last 5 years she owned it, then the first $250,000 of capital gain is not taxable, and if no 1099-S is issued reporting proceeds from the sale, it doesn't even have to be reported on *any* tax return. But this holds true only if your daughter is the owner of the house prior to the sale.
Now by all means, if you have no problem paying taxes when you otherwise don't need to, I'm certain the IRS (and state if the state taxes personal income) won't have any issues with that. (But the current lender will have issues with a quit claim on their collateral - count on it.)
There's another thing too and this does matter.
If your daughter quit claims the property to you, then she's got some IRS forms to file. The IRS will consider the house as "gifted" to you. Since there's no doubt the gifted value is more than $15,000 she will need to file a gift tax return with the IRS. Basically, if a person gifts more than $15,000 to another person in any one tax year, then the gift return is required to be filed with the IRS. (Can't speak for the state, but chances are there's some kind of requirement there also.)
Now the name of the IRS Form 709 - Gift Tax Return is somewhat of a misnomer. There is no actual "gift tax" paid or imposed. All it does is subtract from the lifetime limit of $5.2M a person can leave to another person through inheritance tax free, when they pass.
There's another option too that will keep things legal and won't require any quit claims or 709 returns.
If my daughter does not sell her house within two weeks she loses the option to purchase a new home out of state.
So buy it from her! It's quite apparent (to me anyway) that you have the cash to do so in sufficient amount that she can pay off the loan. What you do with any profits you realize from your sale after fixing it up, is between you and your daughter.
