But you'll want to switch to a console for duties
While I've already spoken about the general quality of the PS4 port for Final Fantasy XIV: A Realm Reborn, I really got a chance to dig into the remote play feature for the first time today and get some extensive testing in. I took my level 47 Dragoon for a spin with some general duties and quests, and found that while the slight lag isn't ideal for the former, the latter works out just fine.
The fact remains that remote play isn't perfect -- for now, there's always going to be some slight lag when beaming all of that data to the Vita, and for dungeons where three other players (at minimum) are relying on you it can be a pain. Even in lower level duties I found that it was annoying to dodge enemy attacks even if they were telegraphed, because they would show up a half a second too late and I wouldn't get the chance to move out of the way fast enough.
In terms of everything else though, leveling and questing (even at a high level like 47) is completely doable. The left and right triggers will function as L2 and R2 respectively, and the back touchpad has four possible combinations -- top left/top right for L1/R1, and bottom left/bottom right for L3/R3. Dragging your finger across the screen will conveniently function as the DualShock 4's touchpad, which lets you move the on-screen mouse around, and touching triggers a left click motion.
Since the bulk of your actions are going to be done by combinations of L2/R2 and the face buttons, acclimating yourself to simpler tasks doesn't take long. If you're itching to get started on the PS4, don't forget that you can transfer over your PS3 license.