Here is the simple cabinet that the seller included with a used DeWalt planer when i bought it. The seller's husband was the original owner, and built the cabinet for himself.
It isn't Baltic Birch, but the 3/4 inch plywood case is rigid and strong. I plan to add drawers someday. I do not know how he used the open space, or what he might have put inside.
Based on my cabinet and the weight of the planer, I would use 3/4 inch plywood. Even if it is Baltic Birch, my sense is that 1/2 inch Baltic Birch is too thin for such a tool.
* Planer on top of cabinet.
* View of cabinet.
* Closeup of top.
* Closeup of bottom.
Note: The outfeed side is identical.
Sorry about the mess. It is late, and I wasn't expecting visitors. :-)