You can open another line of credit as soon as everything gets recorded. You will sign all the documentation and the deed actually gets recorded either later that day or the next day. Once you have closed, the lender is done checking your credit. The new credit source will check you out and make sure that your debt to income level is acceptable to them, but most debt is much easier to get than a mortgage.
PLEASE reconsider buying anything on credit after a home closing. You haven't even determined how owning the house will affect your finances. You don't know how easy or hard your mortgage payment is to make, you have no clue about the utilities and upkeep, etc. Don't add to your monthly burden until you know you can truly afford it.
The refrigerator you need, so buy that, but PLEASE hold off on the furniture.