Even if you're qualified, you certainly should not go on a one-way trip to Mars. I believe the rule of the cowboy should be applied when selecting participants in such a journey. First and foremost, eligible candidates should NOT have living family, especially children and/or a spouse. These types of ties are major problems. Candidates should probably also possess an naval or air force background (like astronauts did in the 1960's) as this type of training prepares one for the type of rigorous mental challenges such a trip is sure to present. A science background would help but I would not think it particularly necessary. Scientific equipment training should satisfactorily compensate for the lack of a science background somewhat (teach them to use the equipment and send the data back here).
I honestly hope we're able to explore Mars further using robots before we send a manned mission there. My fear is that men will contaminate Mars before we've (adequately) ruled out the possibility of native life.