Just level Herb / Mining since you'll be able to fly in Azeroth aswell on the trial. Don't complete any quests yet, you'll level up 80 -> 85 only by mining/herbing in Cata zones once your professions will be high enough (425+ or so).
10 days should be enough to get 525 on both Herbalism and Mining and full xp bar from 80 to 81. Only quests you have to complete after you'll pay your subscription and buy Cataclysm are the ones that will unlock the portals to Mount Hyjal, Deepholm, Uldum, Twilight Highlands, Vash'jir.
Good luck
