What a sweet litle girl you have! Yes, most styles lately are low rise. However, mid rise is certainly coming back this fall! Anything over an 8 inch rise is considered a high rise these days. AJ jeans is a high rise jean however they go for about 150 a pair at Nordstrom. You may be able to find a used or cheaper pair on Ebay. I also recomemnd trouser style jeans. www.delias.com is a cute and very affordable online site for teenagers. Most of the jeans are lowrise but if you go to the pants section, they have more conservative style cuts. Lee jeans and Old Navy boycut jeans are very nice mid rise jeans. They sell for about $30-$50. Also, the current style is long shirts, so if she doesn't mind a mid rise, the long top will cover any bit of belly button that may peek out above the jean.
I also recommend going to Neiman's or Nordstroms where the personal shoppers are VERY helpful. Tell them you are looking for a mid to high rise jean. Have your daughter try on the different brands they suggest and then write down the brand name,the cut of the jean,AND the size that fits her best. Then get online and do a search to see if you can find either similar or the same ones but cheaper on ebay or another site.
By the way, here is an article you may find interesting!
http://www.msnbc.msn.com/id/11902222/site/newsweek/