I know it's tough to think logically about financial issues when you've been hit by an emotional mack truck, but I want to walk you through a few scenarios.

It sounds like, in this short marriage, the house and any debts are the only real things to be split up - correct? And I believe you said she wants to leave the house to you?

Consider this carefully for the moment. I'm assuming the house purchase is fairly recent, so any equity in it is likely just the down payment, IF you're lucky?

So - consider the following scenarios and think CAREFULLY about what is best for you:

A) She keeps the house and buys you out. She would have to be able to qualify for a new loan on her income alone, in order to get you off the mortgage. The absolute worst thing is for you to still be on the mortgage papers but you've signed the house over to her - NEVER do that. If she defaults, you're on the hook for a loan on a house you don't own.

B) YOU keep the house and buy HER out. Again, normally YOU would have to qualify for a new loan, which you won't be able to do with your recent work history, I'm guessing. And unless there's a substantial amount of equity in the home, it could be risky.
Let's take a hypothetical scenario: you own a house worth $100k and had put 20k down so the mortgage is 80k. You pay her $10k and refi the house to a 90k mortgage to cover it. Next year you're out of work again and can't afford to keep the house, so you sell it. After you pay 6k in realtor's fees, plus closing costs for the loan and money to spruce up the house to sell - you probably walk away with zero in your pocket - ASSuming you can sell it for the original $100k. If the market has dropped, you could LOSE money. And SHE walked away with 10k.

Let's take another hypothetical - still a 100k house with an 80k mortgage. You keep the house and she agrees to give up her equity in the home to you. She also agrees to leave her name on the mortgage for 2 years (which would be STUPID on HER part but hey, if she's in such a hurry to get out she might be dumb enough to agree to it). If you are still forced to sell in a year, at least you have some equity to work with and MIGHT come out a tiny bit ahead.

Third scenario - you agree to sell the house and split the profit, if any. This way you are both equally on the hook if you lose money on the house.

Think VERY carefully. If you've only owned the house a short time, I rather doubt it makes any sense for either of you to keep it.