I upgraded from an older model Pentax (*ist DL) to the K10D a few months ago... for your daughter, I think you might want to consider looking at the K100D or K100D Super. The body will be a little smaller, which will likely make it more comfortable for her to hold, and there are fewer on-body controls to worry about -- it may be a little daunting to go from a point-and-shoot to a DSLR body.
Now, granted, you can set the K10D to Program or Automatic mode and click away, and you can even customize the program mode to suit your useage in the menu (you have options for fastest shutter, best sharpness for the lens attached, and one other that is escaping me), but the "portrait," "sports," "landscapes" scene dial modes that are common on entry-level DSLRs and point and shoots aren't there on the K10D.
The other thing you want to look at is glass. The basic 18-55mm kit lens is not a terrible lens, it's certainly no worse than the entry level Canon or Nikon equivalents, but it might not be a good option for sports (horse racing) work, as it doesn't have a lot of reach or speed.
You may want to consider starting out with the 16-45mm f/4 rather than the kit lens -- it's a bit wider on the wide end, gets good marks from its owners, and and is actually pretty affordable right now (around $300 after the $100 rebate).
Unfortunately, Pentax does not have a good telezoom in production right now; they have a 60-250mm f/4 on their roadmap, but I wouldn't expect it until next year, and it's probably going to retail in the thousand dollar range (educated conjecture on my part). A lot of nature photographers using the Pentax system opt for the "Bigma" -- the Sigma 50-500mm, but again, that's a $1000 lens.
Now, there is always the option of using older, manual focus lenses, but that is more of a task for the enthusiast than the casual shooter. I don't know what it's like to take photos of a horse race, but I'm generally able to do pretty well at a baseball game using a 300mm manual lens and a 1.4x teleconverter. (see here for an example shot --
http://www.downeffect.com/jim/gallery/displayimage.php?album=184&pos=71 )
Let me know if you have any questions about the system... of the currently available lenses, I have first-hand experience with the 14mm DA, 18-55mm DA, 31mm FA Limited, 77mm FA limited, and the 50-135mm DA*. I think I might be one of the few Pentax owners here on Macrumors.
Jim