At level 20 you shouldn't have too much trouble healing for Deadmines, even without the gear. (If you were, say, level 16, I might worry.)
So long as you explain to the group that this is your first time healing, and keep an eye on your mana, you should be fine. A couple other tips--see if you can bring along a damage class that can also heal (my first time healing Deadmines, I went with a Shaman friend) so you have backup when you go oom. Also, there are several healing items that drop in Deadmines, and anything with intellect should be good for you if no one else needs it. Just ask the group first, most are pretty reasonable about letting you pick up whatever random assortment of gear will help you keep them alive. :)