I'd say a good rule of thumb is to upgrade your gear every 5 levels. If you do your class quests, they will upgrade the weapon for you. While you CAN just use gear from dungeons, you're likely not going to do so well in the level 15 dungeons in level 1 gear. That argument also assumes you're regularly running dungeons. If you're running FATEs to level like 99.9% of the population, you're not getting gear as you level.

So, yeah. Upgrade every 5 levels or so.