That's what the database tab is for. It will show you most (I'd say "all", but the database does have some missing quests) of the available quests in your current zone. I believe if it has a number "0" in front of it, it means that the quest is seasonal. The rest should have a level number in front of them.
The "History" tab will tell you what quests you have completed and I think this tab, also, goes by your current zone.
Open your main Carbonite folder in the "AddOns" folder, and find the "CarboniteReadMe.txt" file. Open it in any plain text editor (IE: Notepad) and, well, read it. Lot's of information in there. All the good stuff comes after the installation instructions. ;^)
I would like to suggest that you take a look at
LightHeaded. It's an addon that has a database of WoWHead comments for quests so you can check them in-game.