Disassembly should be done in reverse order.
Do note though that IKEA furniture doesn't usually like being disassembled and reassembled. (I've had mixed success in the past.)
I'd advise the following steps:
- Using permanent marker in the back to mark out where every part was, different colours vertically and numbered horizontally.
- Remove the thicker top and bottom planks that secure everything together.
- Remove the thicker side planks.
- Remove thinner planks layer by layer.
It should be fairly easy to just pull the smaller planks and leave the dowels in place for later reassembly.
Once the small planks have been removed the wider plank should slide right off.
- Reassemble in reverse order using the marker notes to determine where the various parts came from.
I'm currently unable to offer a visual aid but if what I've described above is unclear, let me know and I'll create a visual aid when I'm home.
I just found a YouTube video which uses more or less the above disassembly method.