My suggestion would be to just let your daughter go at her own pace and get comfortable, then gently encourage her to try newer things, or the same things on different horses.
I'm kind of a timid rider myself. I don't cling to the saddle horn when I ride western, and I do some small jumps, etc., but I'm just more cautious than most other riders I know. I'm the one who goes to the gymkhana style show and says "He's a little fussy, I think we'll just walk the barrel pattern today", instead of "He's a little fussy, OPEN THE THROTTLE!" I'm sure your daughter will build some more confidence with time. You said that she's only been riding for a year? That's a while, but in the grand scheme of riding it isn't that long. Riding is meant to be fun, and too much pressure can wipe that fun away in a heartbeat. I have heard of the John Lyons team penning method, Juniper, and that would be a great idea. I have heard of horse soccer as well, and in my 4-H club, we occasionally play what we have dubbed "horseball", basically throwing a hackey sack or other small ball back and forth on horseback, sheer fun. It gets the mind off of "what if, what if," and on to having fun with the horse.
Good luck to you and your daughter!
P.S. If her fear is of falling, maybe take some gymnastics lessons and/or otherwise learning how to fall correctly will boost her confidence. I also like one rein stops on horses to instill confidence in teh ability to stop them no matter what, and there are also several emergency dismounts that can be fun to learn and will show your daughter that if she needs to, she can be off in an instant.
Hey! I wrote a novel! Lol