Look inside your fireplace, trace the gas line and see where it goes. Main gas line coming in, then it goes to key valve, and then to burner?. There should be some kind of union installed somewhere so you can easily take apart the pipe in case you have to replace gas valve or burner.
I see there is a cover surrounding the valve. That's good, that can just pop off and back on.
Look for a union (which is a big looking nut). (Post pics) This is where you can easily take the pipe apart to replace the valve. If you have a union report back to us.
If there is no union, then this is not a diy project and you should call a professional master plumber and have him install one when he replaces the valve. That way if the valve or burner ever needs to be replaced, you or the next home owner can do it yourself. Or you can ask him if he can rebuild it somehow to make it work for now to get you through the winter.
Those key valves eventually wear out over time and the key does not fit properly over them anymore to turn gas off and on, like in your case.
Other than that, stay tuned. Other people are reading this thread as well. You might be lucky enough to have a master plumber respond or have someone that has had a similar situation.
I am not a master plumber just a diy homeowner like you. I can only speak of my similar situation. I was lucky enough to have a union. Every situation is different. Some of those old fireplaces are really hard to get into.