MDF can be planed, IME the outer face layers have a finer finish than the inner ones
There are no layers in MDF, or any fibreboard. The top and bottom surfaces are super-smooth because of the manufacturing process (compression of the wood fibres and adhesives). As soon as that surface is removed, the looser fibres, as found on the sides of a board, become exposed. These exposed surfaces can be shaped with a plane, but the finish will always be pretty poor. I suppose they could be sprayed with a lacquer and sanded back to a decent finish, but all of that seems like quite a lot of work – it may be cheaper and easier to just replace the MDF. Don’t know the design of the bed in question, but it may be a simple matter of adjusting the joints/edges on some, rather than all, panels.
Always wear an appropriate mask when working with MDF, and even a disposable suit (or wash your clothes immediately afterwards) if you’re doing lots of cuts/sanding. The dust is awful and one suspects that it’ll fall foul of some degree of regulation at some point in the not-too-distant future.
