Yes, you can do this but here are a few things to be careful about.
1) Depending on the grain direction (flat, rift, quartered) you could wind up with a warped body if you just slap those two pieces together. Maybe not today, but down the road as the humidity changes. I will assume for the moment that the material you have is what is known as flat sawn, or plane cut. That means the rings of the tree are running across the width of the board. At a minimum you should make sure the rings are oriented opposite each other when you glue up. Like this () or this )(. Not this (( or this )). For even better warp management another layer in the center of a similar or contrasting wood can be bitchin' looking and also stabilize the lamination. This piece should be oriented with the long grain 90 degrees to the outer laminations. (l)
2) You need lot's of clamps or a vacuum press to do a proper job of lamination. Wood clamps put a lot of pressure in a small area. You are trying to clamp a large area and must distribute the force of the clamps over a wide area. The math is against you and furthermore, leverage is against you as you try to clamp the center of the board. Lot's of deep throat clamps is the ticket. Better yet, glue up the two halves to the thickness you want and then join them together later. Setting them down on the floor and putting dumbell weights on them is a dumbell thing to do too. Again, the pounds per square inch math gets you. A 100 pound weight on an 18 X 24 lamination is less than 1/4 of a pound per square inch of pressure.
3) Don't discount the hydrostatic pressure of the glue before it dries. Ever notice when you glue up even two 3/4" pieces of wood together that you can clean up the squeeze out only to have more appear a minute later? That glue is coming from only 3/8" or less away and has a hell of a time migrating that far. Now, how much excess glue is puddling up inside that 18" wide lamination you are considering? Just the right amount of glue is the thing to do here. I use a paint roller followed by a very fine toothed trowel to apply glue on large laminations. The roller controls the amount of glue applied and the trowel raises ridges that will then flatten out as pressure is applied. The thing you don't want is a puddle of glue that has no where to go.
4) Install some locating dowels in the waste areas of your lamination to keep things in line while the glue is setting up. Slippery stuff that glue, and it may just move a bit on you even after the last clamp is tightened.
5) I'll get some argument on this one, but it is a good idea (in my opinion) to sprits a little water on the unglued side of the board just prior to applying the glue. Don't soak it. All you are trying to do is introduce the same amount of moisture to the unglued side as you are with the glue on the other side. This keeps the board from warping away from the glue joint as wood that is glued tends to do.
6) Last thought. Use standard Titebond and not the II or III or any of the waterproof stuff. I won't get into it here. Just trust me.
Pardon my chicken little approach to this. Been doing it too long and seen all kinds of good wood go in the scrap pile that could have been on stage instead.
Greg N