Day Trip to Gobekli Tepe

I seriously contemplated going to Gobekli Tepe from Antalya last spring. I had already pretty much decided a few days before the earthquake in February that it was more than I wanted to take on, and the earthquake sealed the deal. The logistics were too much, it was too close to the Syrian border, ...

If I am not mistaken, the Turkey tour ends in Kudasi in the morning, and presumably you would fly out of Izmir. Is there a direct flight from Izmir to Sanliurfa? Turkish Airlines routes most flights from Istanbul, but Pegasus might have a direct flight. I am guessing you have already done your homework there.

Even if you can make the flights work, that's a lot to cram into a single day. I would be more inclined to spend the night in Sanliurfa. (Of course, I lean toward slow travel. I don't like to rush.)

Also, how are your Turkish language skills? You are not going to find as many English speakers as you would on the main tour.

I have never had any issues as a solo female traveler in Turkey. Keep in mind, though, that Sanliurfa/Gobekli Tepe, is in a much more conservative area than the main tour routes.

I did research and found it's easiest to fly from Istanbul and low cost. You can rent a car at destination for low price.
I assume of you show respect for the faithful is a must. After all this is the also the home of founder of three major religions. Abraham lived there.
The museum in town was closed due to flooding earlier this year but should be open by now. You can see much at both locations.