I found a manual online and I think I know what you have. LP with manual control (no remote).
Observe the pilot flame while trying to light it, you need a good strong flame that contacts the thermocouple. If it doesn't get hot enough it will not produce enough voltage to hold the pilot valve open in the gas valve. It is generating a voltage of less than 1 volt to keep the pilot valve going, so it is critical for it to be a good flame.
Make sure it is burning strong out the end of the pilot burner, not a lazy flame that sort of curves up and barely touches the thermocouple. If that is the case, you need to clean the pilot burner first. (If it has never been cleaned it probably needs it anyway.)
With gas off, try using a small brush and some compressed air to clean any soot, dirt etc. from the pilot burner. (Look for the little tiny orifices down in the burner where the pilot gas comes out) .
After a good cleaning, try relighting the pilot and see if it holds in. If it does not, you probably need a new thermocouple. You should be able to pick one up at a hardware store or a stove/fireplace shop.
I don't know how accessible your pilot is, you may have to remove it to clean it good. Make sure the gas is off and when you reinstall, if you had to remove the pilot gas line, make sure the connection is tight.
If you are not comfortable doing any of these things, don't feel bad about getting a furnace guy out there to take a look at it.
Check the easy stuff first. Good luck with your fireplace. Hope this helps.
Let me know if you need further help.