What do I need to do to raise a subfloor?
You could simply install a transition piece between the two rooms.

But if you're determined to get them to match up, then 1/4" luann board will do nicely.  Glue and screw - 1/4 bead of glue distributed evenly over each board, screws on a 1 foot grid.

NOT going overboard is what leads to squeaky, shifting sub-floors that make for a shoddy looking finished product.