It's odd, but I didn't feel as if my mage was particularly weak at that level. If you are going frost, it's true that some of the damage advantages take a bit to stack up in terms of talents, but I still didn't find it hard against on-level mobs -- I died in cases where I did something wrong (ie, forget to use a skill, bit off too much) or got an unlucky add, but nothing more than that. I could also take on one mob of 1-2 higher levels, and win, but it would cost a lot of mana.
As a frostie, what I would do is be sure to start at max range -- don't get lazy or sloppy about that, setting up at max range is a critical skill to learn as a mage, whatever spec you are ... move around, back up as needed to get to max range -- and then frostbolt, frostbolt, frostbolt -- if the mob isn't already frozen, then FN and strafe away, then frostbolt, frostbolt and, if needed, fire blast and/or wand. Frostbolt is a relatively low mana cost spell for a nuke, and if you put the five points into it it is a very fast cast as well .. in my view, for both of those reasons, it's meant to be spammed. Using this frostbolt-spam rotation, I found I would end most on-level fights with a good amount of mana left, while fights against higher levels would take more mana and result in some drinking downtime. But I can't remember ever going OOM or, again, getting killed unless I made a mistake, or got an unlucky add.
As a fire spec, a few levels later (in the 20s), I would open with fireball, fireball (and if time, a third one or a scorch), then FN and strafe, scorch, fire blast, wand. On tougher ones I would open with pyroblast. Now of course, with fire, you are going to burn through mana more quickly, so you have to be careful, and you will be drinking more (at least that's how I've found it), but that rotation isn't "weak" really.