There are a few quests (most of your class/job quests and a few main storyline quests) that include a solo-only instance, but those are short, few and far between. Otherwise you can group with her through everything. In dungeons, you'll need additional people to also join your group, as those are for four or eight players.

In order to group together for the first 15 levels, however, you should pick starting classes that begin in the same city. (You can change classes later if you want something else.)
Archer, Lancer, and Conjurer start in Gridania. Gladiator, Pugilist, and Thaumaturge start in Ul'dah. Arcanist and Marauder start in Limsa Lominsa.