My husband moved out; if he signs a quitclaim deed, and I buy the home but am still married and something happens to me, does it go to him?

Generally most states do not allow for you to disinherit a spouse completely.  Spouses who are left out of Wills are almost always given a "right of election" against the estate of their partner who has written them out of a Will or a portion of the estate if they die without a will under the intesacy laws.   Also, the quitclaim deed is considered the lowest form of deed.  That said it is also commonly used in divorce actions when there has been an agreement signed that gives sole ownership to one of the parties.

If you don't want to actually get divorced but want to make sure that what you own is protected you should at least enter in to a separation agreement (and each of you should have legal representation) that states how you are dividing the joint property (of your own free will) and helps show that from the date signed forward you are not considered "married" for estate purposes. 

You should also immediately have an attorney prepare a Will for you. There may also be a way that the law in New Hampshire allows a party to consent in some way to allow the property to be Willed to someone other than the surviving spouse and to give up their right of election.  Seek legal counsel in your area.