Hi, Lee, and welcome to the forum. You certainly landed in the right place. (Pun intended)
The Kymera is an intermediate to advanced kite because of its tricking capability, like a knife edge on your Ultra300, but it will fly like a high-wing floater for the beginner with the proper adjustment. John Barresi, the guy who owns and runs this forum, is the one who designed that kite, so you're definitely in the right place. I'm more of a quad-line guy so I'll let John and the other, more experienced, flyers guide you through most of the beginning steps. You will also need a stake to anchor the kite and lines when you are not actively flying. A long cheap screwdriver will do. The most important thing to remember is when you are about to crash, (it's not as bad as an RC crash), to give to the kite. Move your hands, arms and body forward briskly to lessen the force of impact. Most duals can take a few hits and are usually designed so that the spine will disengage from the sail in the event of hard impact, like rubber band mount wings on some beginner floaters.
As far as a kite for your daughter goes, I recommend pretty much any single line delta in the 3-foot span and under range. Stay away from anything with a lot of pull. If you spend 25 - 30 dollars on it you'll have a keeper. There are so many different single line kites that it boggles the mind and choosing one over another is determined pretty much by whatever moves you.
Remember, the main reason to fly is having fun. Smile, and don't forget to breathe.