Noobish Level Sync and Gear Question

So my main is a level 50 White Mage and I'd like to go back and run some early level (particularly Tam Tara) dungeons again to try and complete my Acolyte's set for vanity. My question is, as a healer, do I NEED to assign a new gear set with appropriate level gear for the dungeons' Level Sync, or can I just stay in my Vanya robes? I don't care so much about look, I just want to make sure I'm not gimping the party and remain a good and effective healer. I know this is a very noob question, but I'm not the most experienced at MMO's and Google searches have been less than helpful....

Your gear syncs with you so don't worry.

That's what I thought I just wanted to make sure. Thanks for the swift and helpful reply :)