You don't have to worry about quest EXP running out. There are plenty of other, faster, ways to level. Levequests, FATEs, Palace of the Dead, and dungeons are all quicker. Look those up if you don't know what they are.

Additionally, you get an EXP bonus on combat classes when you already have another combat class at a higher level. So it will be quicker to level that second job! There is an EXP bonus ring you can get from Hall of the Novice at lv 15. DO THAT if you haven't already. That ring is effective up to lv 30.

I do second the advice of focusing on main quests until your first level cap though. The main quest line is very long and unlocks all kinds of features you'll want to get ASAP... airships, levequests, grand company, your mount, lots of dungeons, beast tribe quests, flying, new areas, lore vendors, and on and on. Just following the main quest will mostly keep you near the level you need to be for the line and the gaps can be filled with your choice of sidequests or other leveling methods. There is no point in diving into all the sidequests the first time around as it will just slow you down overall. I made that mistake up until about lv 20. Of course, if you're having fun exploring side quests and just want to take your time, then do it your way! Just know that you don't need to worry about it!