Are you positive on that 81/2 Womens sized shoe ? Does that shoe fit really well ? Brand sizing can vary greatly. Smaller women often wear junior boots. Your daughter hasn't broken the 100 # mark yet, and not really even the 5' mark. But she is 14 yrs old. So the brain counts.
Take her shopping to a really good (couple of) ski shops with good boot fitters & gear guys. She's 14 , has 4 years until she's considered an adult. Get her involved in learning from the start of listening, thinking, processing, trying on, deciding yes/no , keep looking. Let her hear the input, guidance, or sales pitches. Since you have the wallet, you get the final say. But, she's old enough to be educated in and experience the learning to become an educated consumer. Making the best decisions she can make. You are growing a skier here. Get her involved with the products and people beyond the internet.
I should qualify this a bit. I can wear 7 1/2 to a 9 1/2 in women's footwear. All depending, and what I chose fits well & very serviceable. Ski boots fit in the same realm.
#2. My 11 yr old has bigger feet than I do & really cool new skis. I'm really wanting to try out his skis & will have to slip on those tad bit bigger boots of his to try out the skis. If I succomb, he'll flip his cookies. He really likes his gear. I didn't pick out one single part of it. It was between him & the bootfitter that also had the cool new skis to go with. I had questions that were answered, but the kid that did NOT WANT new gear was sold on some really great gear that he did in fact need. Killer deal ! And the best part, no matter what, I'm not allowed to carry it, ever!
I've been reminded I am often too subtle. So basically what I'm saying here is, she's 14, take her out shopping, learning, experiencing. At this age, you should not have the majority of input or control over the decision or the purchase. It is a shared thing and product in hand at store with experienced people build the experience and knowledge. Good or bad. But definately create child/parent discussion, communication & understanding. You are growing a skier. A pretty independent yet interdependant sport.