This has come up before and the answer I've always seen was no.
Some things to think about:
Newly pierced ears need to be cleaned several times a day. WDW might not be the best place to remember to do this.
Also, when my DD's got their ears pierced the last few times (more than one piercing in each ear), one of the other things they were told was not to swim for several weeks.
I don't have a link, but you might want to look up webpages for some places that do piercing like Claire's or Piercing Pagoda to check out their information for newly pierced ears.
What some people have done instead of getting the ears pierced at WDW, was to get them pierced long enough before going that you could pick out some cool new earrings at WDW and be able to wear them right away (you can't change newly pierced earrings until quite a few weeks after, to give the ears a chance to heal).