Tight connection at LHR

Hey, everyone. I just booked a flight to go back to Prague in early October, so it’s still pretty far away….but I’m a meticulous planner. I’m flying from DFW-LHR-PRG (my Dallas to London flight is one of the ones that gets to skip security - Flight 20). 1st leg is AA, 2nd is British Airways and it’s on the same ticket. I’ve never been to LHR, but from what I understand is that it’s a pain when connecting through especially if it’s a tight connection. My flight arrives at 9am and departs at 10:15am. I see that there’s another flight to Prague with BA after the one I’m taking that departs at 1:15PM.

Is there a big chance that I’ll miss my flight? I’ve never missed a flight before, so what happens if that happens? Do they usually put you on the next one? Also, am I better off trying to see if they will let us take the 1:15 flight rather than the 10:15 one? Is it possible to make my flight because we get to skip security?

I know at LHR, you can’t just run from terminal to terminal. How long does the transportation usually take and is it readily available or would we have to wait for it?

Thanks!