only issue with mdf is that the dust isn’t very good for you
MDF is the MMR of the carpentry world. There’s not really any credible concerns with using it. Using it is fine, dust of any kind is something you want to control. The amount you can create making one kids bed is of little concern.
Birch ply is the most attractive stuff to use, mainly because the ply thickness are uniform (same thickness and same wood throughout) hardwood faced ply has an ok face but I think the cut edges are ugly, the inner plys are a different wood to the face and different thickness and often gappy. If find the edges of hardwood ply a bit too keen to splinter.
Structural spruce ply is nice to use, it has the edge quality of birch, with uniform plys. It’s rougher and knottier than the others but if you choose a good sheet (some have one better quality face) can be quite attractive – it almost looks like a characature of wood.
Use mdf though. Use extraction with a circular saw, with a jigsaw slow the blade right down and it comes off as little chips rather than fine dust. Slow speeds with a router work well for the same reason