Determine depth of laminate flooring
Laminate floors have a gap around the edges for expansion, which is covered by quarter round or a baseboard. You can gently remove a short run of quarter round or baseboards and measure the laminate thickness that way.

Since you're removing some of the laminate, you'll need to pull the baseboards/quarter round up anyway so you can lay your new flooring closer to the wall.

Or, as @diceless points out in the comments below, removing a floor register would offer an even easier hassle-free method for determining laminate thickness.