Haven't used the Jolly Phonics but somewhat familiar with it. Yes I would say it expects the child to have more skills than your child probably has now for doing all the parts - ie printing, cutting, etc.

The old way of teaching reading through phonics involved looking at word groups. If she picks up sight words quickly and knows the letter sounds she might enjoy that. You can then make games with sorting the words etc. There are sites on the computer with ideas for teaching word families - ie at - bat, cat, mat, rat, etc.