I'm a newbie myself (NQT here) but I'm fairly confident the more experienced will back me up. No, you cannot hope to do a Masters and a PGCE at the same time. I doubt any PGCE admissions criteria would allow it. In fact, I believe you would be insane to attempt to do so.
I spent the last academic year embroiled in the organised madness that is a PGCE. Yeah, it has some less pressured points (on my course the first 4 weeks or so were fairly chill) but the majority of the course is spent juggling the demands of placements which are in effect like doing a full-time job (yes you teach a reduced timetable, but you need extra time to plan and mark effectively as you learn this 'on the job') with the more academic demands of essays. You are being observed regularly, you are under pressure, you are impacting the lives of your students for good or ill, your personal/social life may suffer, there is never enough time for everything you need to do.
In my younger days I did part of an MA course (dropped out as it wasn't for me) and although it is less 'intense' than a PGCE it is most definitely not something to take lightly, especially writing your dissertation.
And finally - old at 25?? I took my PGCE at the grand age of 32 and I was far from the oldest. Many on the course were late 20s, 30s, even - gasp - 40s and beyond. Slow down. It's not a race!