My DS only has a single bed, and we have always used a double doona.
If you are having trouble finding KS covers, sheets etc, have a look on Amazon they have a great range of KS stuff at reasonable prices. The reason i knwo this is because we are getting DS a KS soon and wanted to make sure you could what was needed as i know furniture places and spotlight, target etc do not have a great range of KS stuff.
We used to have KS as kids. Mum would get us KS sheets, but double sized doona covers. I believe in catalogues I have seen more kid prints in KS, but that might be at Pillow Talk and the speciality sheet stores
ALL the Doonas and covers in our house are 1 size larger than the bed size.
The King Single has a double.
The double has a Queen.
The Queen has a King.
The king has a super king.
I Like the overhang - I think it looks much neater, and covers the mattress much better... plus there is far more Doona there for cold nights, which means it's less likely to fall off OR get stolen by DH lol.