How scared should I be about DPS?

[Shurrikhan]

He's correct. You should be focused on three things, in order:
1. Not dying
2. Healing
3. DPS

This is true. That said, I've consistently seen people improve far more quickly by working backwards from the final goal (dps).

As a healer, you shouldn't be thinking "When can I dps?" Not only is it the overwhelming majority of GCDs, but also tends to feel more ambiguous in such terms.
Within a given window, the question should be "How much damage will I have to undo?" (This will depend on your cohealer, tank, and idiocy of any and all players among AoEs only if such would otherwise kill them.)
Likewise, you shouldn't be thinking, "When can't I move?" so much as "Where do I need to be next?"