I don't know about Limsa, but I did go on foot to Gridania on my Thaumaturge from Ul'Dah at LV 10 to level up Conjurer for Cure and Protect and use Cure as self-healing skill. I could not do LV 10 story quest because it was too hard so I could not go further. So I could not use the ferry and air ships. But after I unlocked Conjuror and got Cure, I could self-heal and I managed to do LV 10 story quest after.