And since when is it impossible to finish a dungeon short-handed? If the person dropping is a DPS then the fights just take longer. If the person dropping is the tank then a DPS becomes the new tank and the healer has to work harder(splitting the enmity on trash pulls can also help sometimes). If the person dropping is the healer then the tank needs to maximize their cooldown effectiveness and self-sustain options while the DPS burn as hard as they can so fights dont drag. Not every combo is equally doable in every dungeon, but few of them are outright impossible - just different degrees of challenging.

OP, i peaked at your character(to make sure you actually had your job stone). You should upgrade your sword. Your shield and jewelry arent stellar(your armor is "okish" but also a fair ways below whats easily available), but your sword is probly holding you back. If people are quitting on you a lot then its likely this(your gear) is part of the problem.