PRG is one of those airports where departing and arriving passengers mingle airside, hence security at the gate. But... the terminal is split between Schengen and non-Schengen. Although it’s one big building, it’s split into a nominal Terminal 1 and 2. As you’re arriving from DOH (non Schengen) and departing to BRS (also non-Schengen) you should be in the correct part of the terminal to make this easy for you.
I’m assuming you’re HBO and can get a mobile BP for your EZY flight.