You cant tile over pergo for a variety of reasons, The Pergo floats so the the tiles will move and crack; the Pergo has a finish that will resist thinset bond to it: The pergo is a slat format rather than a homogeneous piece of wood like plywood and will move with the seasons causing the tile to crack. No need to go any further.

Remove the pergo, report back with the makeup of the subfloor, is it plywood or cement slab?

Pergo is usually not glued down it floats so taking it up should be a snap, but you will have to remove the toilet and vanity to get it all out. The height transition o to another floor is best accomplished with a marble saddle in the doorway.