To make sure, I just made an online saving slot with a new character, played a bit and then deleted it, which worked fine for me. You are logged into the website for both occasions are you? Both the website itself and the online game saving? It should work fine then. =)
Besides, you can restart the game, by making a new online saving slot and start from there. The game and the website should follow that saving slot and grant you the Quests as normal when they are achieved. =)