I would guess that they would have appropriate terrain at Alta for your daughter to be able to ride the lift. If not, and she really wants to ride one, do a round trip. I've done that with my daughter. Or take her to Snowbird and ride the tram up and back with her.
I know a lot of people here don't like harnesses, but I use one for my daughter. If used *properly*, they can be a great asset. The idea is only to use it as a safety device. You don't want to let her "hang" on it all the way down the hill. And if you get one, get the kind that straps around the upper legs and waist. NOT the chest harness... unless you want
to slam your daughter onto her back
: . My daughter never used the tip locks (edgie-wedgies). We tried for half a run, but they did more harm than good because she was able to hold a solid wedge already. When I ski with my daughter with the harness, I either ski beside her with a lot of slack in the lines or just let go and let it drag. This way, if she gets tired and and starts to accelerate too much, I can reel her in. But even when I do this, it's only to get her back to a slow speed. Then I take the pressure off the lines. Once in a while I've had to just stop her because she wigged out and wouldn't resond to any requests to make a wedge or turn. When I do that, I stop her fairly quickly, then just sit with her for a while and talk to her and calm her down until she's ready to go on her own again.
The harness is also great for towing her around the flats. Do NOT (let me repeat that) DO NOT
use your poles and tow her around with them! Also do NOT try to ski with both of you holding a ski pole, thinking that it will help her. She'll just fall on her back, or worse yet, you'll cross tails with her and tear up her kness. Not a good way to end a vacation. If you are going to be skiing with your daughter, leave your poles inside or park them in the snow somewhere safe. Don't try to handle your daughter and your poles at the same time.
Definitely use a carpeted area in your house to put her skis on and have her practice stuff.