Too Young To Be Grumpy

I've spent this afternoon trying to think my way around cupboards and the physics involved. I'm new to DIY and putting up cupboards is a new skill I'm attempting to acquire. Of course, I don't do things the easy way, either. No, this cupboard only has two sides and sits in a corner between two walls - coving on both, and pipes in the corner. The doors have to be offset from the wall so they don't hit the curtain pole. I've put a false bottom in the design so we can have lights underneath, and it's made from standard veneered chipboard. I've built the bottom, with the false bottom, and the side - but I'm worried that those things on their own will be too heavy, let alone with the weighty veneered MDF doors we've bought. Yikes. I see a one-time collapsable design approaching.