Like Jon said, center the doorway wood "threshold" or at least keep the wood farther towards the inside of the door than the hall side of the door. Most likely the door will be open 90% of the time, so not a big issue how far the wood "threshold" intrudes into the laundry.
That said, if the laundry room is going to end up in ceramic tile you will certainly have some height issues do deal with. Before pondering this threshold issue, you first need to figure out what the finished tile height will be if it is installed properly.
The tile height is your starting point on the issue you are describing to us.
Tile installation may involve removing that plywood and installing a cement backer board, or installing backer board on top of the existing plywood. Add the 1/2 backer board on top of that plywood, plus 3/8" tile thickness and you now need a floor transition between the hallway and laundry of about 7/8 of an inch.
If the subfloor in the laundry is strong enough, you might remove the plywood, then install backer board, then the tile........... but the tile will still add some additional height above that hallway surface.
I think that first step is that you need some input from a trusted tile installer so he can evaluate the options based on the strength of your homes flooring system. A good tile installer will tell you what the minimum installed height of the laundry room will be, based on what he sees on your homes age and floor joist span and construction. I think that is the first thing you need to figure out.