How can I build a bed frame out of palettes?
Believe it or not, there is an entire Pinterest page dedicated to beds made out of pallets. There are no instructions, but plenty of designs in addition to your IKEA model that you can use for inspiration. Some involve simply stacking the pallets in various configurations, but several of them are quite stylish and it's pretty easy to see how they disassembled some pallets and screwed them back together to make a nice frame.

Have a look!

Pallet Beds