Joni,
I don't think there is a person on the planet that doesn't harbor doubts about a new project or endeavor.
I don't care if they tell you from 7AM to 11PM that they KNOW their new (whatever) is going to work and they are just brimming with confidence... at 3:14AM, their eyes will fly open from a deep sleep and that "twinge" of fear will work down their spine and into their belly.
It's not only completely natural but it's expected. Doubt is a good emotion. It will help force you to be careful and to do things the right way rather than half-arsed.
And you'll encounter prospects that doubt your abilities-- no matter if you've been at this copywriting stuff for 6 hours or 16 years.
Failing isn't bad. I've learned so much more from my failures than I have from my successes. I know that's almost cliché anymore but it's 100% true.
When you come to not only accept failure but appreciate its appearance and the lessons it brings-- then you'll really be on the threshold of something great.
Copywriting is a high failure business no matter what anyone says. Many times your efforts will not lead to a big improvement of your prospects business... that's because copywriting is only a piece of the pie-- it ain't the whole thing!
So trudge forward, fall down a few times, get banged up a little and simply carry on towards your goals.