Not that I know of, but even if there is, I would think twice about doing it while away on vacation. Most people are fine but every once in a while, there could be some complication or infection or allergy. Especially with children, I'd rather be at home in case we had to have a doctor look at it. Also, newly pierced ears require extra care and cleaning.
She could pick out some cute earrings to bring back.
Maybe you could make a special voucher for your daughter's birthday saying 'when we return home you can get your ears pierced but for now, select a lovely pair of Disney earrings!' and decorate it with her favourite Disney characters.
Once ears are pierced it takes usually 6-8 weeks before they are allowed to change the earrings so that way she has something to look forward to once she gets home (getting them pierced, then later putting in the special earrings she selected). There are plenty of cute Disney earrings, plastic-y '3d' cartoon Mickey/Minnie heads, Mickey/Minnie heads made of coloured gems, princesses, small silver mickey heads etc Keep in mind that some people are sensitive to the cheaper earrings and may only be able to wear silver or gold.
Happy Birthday to your Daughter and have a great trip!
Even if there was, I wouldn't do it. DD had hers done 2 weeks ago. They were tender for several days and we have to clean them 3 times a day. Do you really want to take time out to do that? I know we will have to when we go in 2 weeks, but we will be a month into it by then.
Also better to do it at a professional location instead of some kiosk or small store in the mall. Go to a place that uses an acutal needle instead of that gun. It might be a bit scary at first, but the needle actually hurts less and heals faster then the gun, which uses sharper earring posts to force its way through the skin.