thinnish wood/mdf/plywood (Brundall NR13)

I have removed a dog flap from a door and now there's a hole in the (quite deep) door. I need to fill in the hole and then paint the door. To get what I need, means buying a big piece of wood/mdf/plywood most of which will end up unused. I'm wondering if anyone has a spare piece of material that I could use please? The hole with overlap is around 27cm by 34cm and I need two pieces. Thank you.