My father wants to quitclaim deed his property over to me before he dies. Can this be done?
"Can be done" and "should be done" are two very different things here. Yes, if we're talking about real estate, your father can simply sign a deed transferring the property to you. (This assumes that your father owns the property himself, outright, which you'll want to make sure of.) However, such a transfer may not be financially wise.
If the property has gone up in value since your father acquired it, you might be better income-tax wise to have your father leave it to you at his death instead of transferring it while he is alive. The reason is something called the tax basis of the property -- that is, the value from which taxable profit is figured when property is sold.
When property is quitclaimed to you, your tax basis is the amount your father paid for it. If you later sell the property, you'd have to pay tax on all the profit that exceeds his purchase price (with some adjustments for improvements and the like). However, if your father leaves the property to you when he dies, your basis is the property's value at your father's death. That's likely to result in a much lower tax bill if you decide to sell.