I second this because the short length of pull will help her develop proper offhand shooting setup.
Third on this (take a close look at my profile pic!) The importance of proper form should not be understated, and the 14"-ish length of pull on an HW30 or other similar adult air rifles is just too long for younger kids. My Embark has proven to be highly accurate and easy to shoot well. It's no Weihrauch, but I found the quality and trigger to be more than adequate and I think it's a great value and fun plinker. The Ruger Explorer is virtually the same gun, but with fiber optic sights (which I don't like). I also love the Slavia 618, which is so small that a 8 year old can shoot it offhand. All of these are really easy to cock.
All that said, for a 12 year old, depending on her size and stature, she may be "big enough" for a proper adult rifle. If that's the case, I can't think of a better choice than the HW30 - easy to cock, accurate as can be, and can be passed along to your great grandchildren. I'd say skip the scope for a start, or put a Williams peep on there, but that's just me. Spiralgroove made a good point above - if you've never shot a high quality springer before, you'll be surprised at how different they are than any of the low cost, big-box store "pellet guns and you may want to keep it yourself! It's not "Chevy vs Cadillac," it's more like comparing a 1985 Yugo versus today's Cadillac.
I'd start by measuring the length of pull on her daisy - most of them are 13.5-14 inches despite being marketed to kids. If that's the case and she's comfortable with it, you can probably skip the youth rifles if budget allows. If the budget is key, then the Embark is probably your best bet - anything in the $100-$200 price range that claims to be "better" is just higher-powered and will likely shoot like a bucket of bolts.
