L.R.
Please listen to those moms who said below that you should ask the dance studio (or individual teacher if it's not at a studio) and get real shoes from a proper ballet supply store or someplace like discountdance.com. If the class is at a studio they may sell shoes right there.
You want shoes that are either real leather or good canvas -- not that shiny polyester stuff that many stores like Target and Walmart sell! That's why you need a dance supply store. Ask the studio whether they prefer leather or canvas. Also ask if the teacher wants "full sole" or "split sole" shoes -- there's a difference in how they work and feel.
You will not get good canvas or leather shoes for dirt-cheap prices; expect to pay more than a few bucks but it shouldn't be too bad. Good shoes will make her much more comfortable and she will focus on dancing, not on how her shoes feel. Good luck and I hope she enjoys her class.