Based on your daughter's weight, she is likely too big for all the kid sized kayaks, or at least at the top of the weight range if she can still fit. That includes the Fun1.5, SideKick, Remix 47, Fuse35, Axiom 6.9, etc.
There are LOTS of kayaks to choose from in the next size up - the Small adult size. Finding one in Utah is possible, but selection is limited. Keep in mind that cockpit sizes can vary widely, so try to find one that fits your daughter's size well. Ultimately you want the kayak "ski boot snug" for better control and easier time learning to roll - without being near the top or over the weight limit at MT mentioned.
There are also lots of opinions on what type of kayak (river runner, creeker, playboat, etc) is better to learn in, I think the biggest key is simply having a kayak for your daughter to start using on the rivers, lakes and pools. She likely outgrow it, either in size or skill, so buying used can be a good move.
There isn't much on KSL classifieds (Utah) right now in the way of used kayaks in the small size but they do pop up now and again. There is a WaveSport ZG 48 package that will likely fit her. A neighbor's kid (age 12) picked up a ZG48 this past winter and it has been his learning kayak. Wasatch Touring in Salt Lake will be selling their demos and old stock in late Aug or Sept at good prices. If you don't mind traveling, there are always some used kayaks in the Boise area, as well as the greater Denver, CO area (ie. Craigslist). A kayak shop in Fort Collins, CO has a demo Zen55, a demo 2Fun, and a new old stock 2014 Jackson Star, all for good prices.
Also, the Utah Whitewater Club rents out the Layton Surf & Swim Wave Pool once a month from fall thru spring. It's a great place for kids (and adults) to practice their rolls and paddling skills, as well as try out different kayaks.