You ask: "IF I DON'T PAY MY MORTGAGE FOR ONE MONTH WILL (IT) GO RIGHT AWAY ON MY CREDIT SCORE?"
The answers from others are all correct--meaning that it's different in each case, depending on who your lender is. But the right thing to do is not be late. The lender has the right, but not the obligation to report you as soon as you are considered delinquent in his eyes. Some do, some don't.
Oddly, you will find that if you want to discuss your situation with a lender, unless you have missed 2 or 3 payments all together, they don't want to hear from you. Meaning that you pretty much need to ruin your credit before they will listen to what you have to say.