So I'm level 13 Mage, and I swear I'm still using equipment from the first few levels.  I'm not finding any drops and the quests don't seem to give anything out, do I have to buy better equipment?  I just don't feel like I'm getting much better as I level.

I didn't play as a mage, but Morrigan was in my party the whole time.  I rarely upgraded her equipment, but she was easily my most valuable character.  Didn't find I needed much equipment for her.  

You should be finding some items dropped by enemies - also, when I played as a mage, I made sure to specialize as an Arcane Warrior, which is basically a mage who can also tank and use swords... if you do that, you can use a sword found in the temple where you find the Urn of Sacred Ashes, designed for Arcane Warriors, which doubles as a magic staff... I believe it's called Spellweaver.

There is a shop called wonders of something.
Also the quarter master in the tower circle.

Colf is thinking of  Wonders of Thedas in Denerim, but I don't know how good the mage robes are.  You might want to try some mods from Dragon Age Nexus. Improved Atmosphere should help with your problem. I also know that when you go to the Alienage, some Tevinter mages there drop some nice robes. And for Morrigan, a side quest that you get in the Circle of Magi culminates in a decent robe, but only she can wear it.

Magi don't really get a lot of equipment upgrades outside of staves. It's more a matter of what kind of mage you want to play over getting better equipment.

As others have stated, most Mage equipment is procured from battles or from the Wonders of Thedas shop. The quarter-master in the circle tower also has the games best staff for sale.

Wonders of Thedas sell some great stuff but they are pretty expensive

Check out the Wonders of Thedas. They have some badass robes and a bunch of other magical shit too for you to stock up on. Personally, I found I didn't even have to buy Lyrium potions, they're all over the damn place. 
 
Anyway, by the time I faced the Archdemon with my mage I had some seriously badass robes on. I can't remember what kind they were though, or I could totally be a big help here.