Good for you! Just don't rush it. Playing the pipes is altogether different from a PC. You've got an instructor, so the transition will be smoothed out some for you.

Your instructor/PM will likely tell you the same things, but here are my suggestions:

Keep up with regular PC practice. Add in a few minutes on the pipes with just one tenor drone. You should soon get to a place where the pitch does not waver.

Add the second tenor drone. Practice tuning them to each other and playing so pitch does not waver. Changes in pressure will be more evident now that there are two drones going.

Cork off both tenors and open up the bass. It consumes air at a rate that will astound a new piper. The bass alone uses more volume of air than both tenors and chanter combined. Play until the pitch does not waver.

Add tenors.

Cork off all drones and sound the chanter. Not much volume of air, but much higher pressure than a PC or even the drones. When you are able to blow steady, tune the chanter.

Add tenors to chanter. Tune them to the chanter.

Add bass. Tune it to the chanter.

Now sit down with your instructor and fiddle with the reeds and bridles so the pipe runs at amximum efficiency. Your should be able to shut off your drones with a sharp squeeze. If you're unable to shut down the drones by overblowing, they're probably consuming way too much air. A more efficient pipe is much easier to play.