Ok so I want to attempt the paladin quest tonight. My question is can a lvl 33 dragoon solo this? I did a squire's test 2 with no problems. I just wanted to know before I try so I dont get killed

Yes; you will need silent oils and prism powders (unless you have ninja and tonko: ichi in which case use that), the former for pugils in the water and the slime at the end of the Davoi run, and the latter for the millions of orcs. There's no combat necessary, just clicking the well, so you should be fine.