The description of the familiar ability Deliver Touch Spells on page 53 of the PHB reads:
If the master is 3rd level or higher, a familiar can deliver touch spells for him. If the master and the familiar are in contact at the time the master casts a touch spell, he can designate his familiar as the "toucher". The familiar can then deliver the touch spell just as the master could. As usual, if the master casts another spell before the touch is delivered, the touch spell dissipates.
It doesn't say "if the master's is caster level 3 or higher" so I'm assuming i can do this now, even though I'll only be a first level mage. It also doesn't specify that this can only be done with arcane spells. So if my reading of this rule is correct, I can take a flying familiar, stand back at a safe distance, and send my familiar flying in above the fray to heal any combatants in my party that might need it.
I just realized I should probably go check the PHB errata. If I find anything there that changes this I'll update this post. In the meantime, how would you rule on this if the rules are correct as I quoted them?
There are no changes to familiar abilities or anything else on page 53 on the most recent version of the Errata, last updated in 2006. However, while the ability description says "If the master is 3rd level or higher", the table on the same page that shows when the familiar gets it's various abilities does say "Master Class Level". Deliver touch spells isn't available until level 3 on that table. So I guess I can't actually do this until I'm a third level wizard. But I can't find anything indicating they only intended this for arcane spells so I still think I ought to be able to do it eventually.