The Vortex of Doom does not have to be a group quest. In fact, from what other players have said, it is easier when you do it solo because there a less Sharks to attack the fisherman you are supposed to save and he doesn't get killed before you can attack. Good luck.
Don't sweat the "group" warning going into those types of quests. If you are up to level (and you probably are if there are no other quests), you will be able to handle the vortex without a group. I believe the warning means that two or more different ships can't enter together unless they have agreed to be a group. They would go in at the same time, but fight individually (I could be wrong on that, but not on the fact that you can take that quest on your own).
I did all the quests at Skull Island and went to see Captain Ahab, but the only quest he gave me is a group quest (the Vortex of Doom). Are there any other quests for level 6?
Fearless Pirate Jeff has an answer for you:
"Captain Ahab gives the player "The Most Dangerous Catch" which can be completed by a solo player. You may be led to believe a vortex is group content because of the warning on entry. This warning is trying to communicate that any non-grouped players (stowaways) on the ship will be teleported back to the last life fountain if the ship enters that vortex. "