My island is 9x4 as well. We are doing a walnut top with a 15" overhang. Many have said 12" is fine but in reality more is better. I think whether or not the island is counter height or bar height makes a difference too. I think with bar height you can get away with less overhang. Also will you be eating at the island regularly?

Our cabinet maker insisted we do a skirt around the seating area. I didn't want corbels to get in the way so we removed them from the plan. Stone is even heavier so you want to make sure you have great support.

I can't imagine not having any kind of support under the 12". I don't know all the rules about this though. I do know that people lean on the edge - even to get up from sitting- and I'd think there would be a possibility of your stone cracking.

12" does not require support in 3cm, but I think it looks better with some sort of support.