Order a ticket online, they pick the transliteration for ø as o, passports transliterate ø to oe - the less ambiguous choice. This generally isn't a problem until you want to travel to one of the APIS countries - USA or UK, which won't let you check in if the name on your passport doesn't match the name on the ticket.
I have tormented many check-in counter staff with this, especially at regional airports that don't see a lot of international travel.