A lot will depend on what they are using for tenders - their own lifeboats or some from shore. I would guess that the tender ride will probably be somewhere in the neighborhood of 15-20 minutes, maybe less. (Lifeboat tenders remind me of bumblebees - big and round and slow.)
You are probably right that shore excursion people will have first dibs, but feel free to ask about how and when to get tender tickets - the shore excursion desk usually handles that, but the purser's office may help out. On a recent cruise, I was able to get a ticket the day before the port call; they announced when they became available.
I envy you, starting out cruising on QM2! Though I'm afraid you will get terribly spoiled - nothing like starting at the top! Have a great time!