Travel documents

First, read the following page carefully about getting a passport for a minor:

Passport for a Minor

Second, every country has its own rules about children traveling with guardians other than their parents. You will need to find out this information. Probably best to contact the local consulates of the countries you want to visit. I'm not sure if there is a single Schengen rule.

You will need at least a passport for her as well as notarized documentationn from both parents that you may legally take the child out of the U.S.

This was from Northwest Airlines' website:

nternational Travel with Minors (including Canada & Mexico)
Because some foreign countries may not permit entry to minors not accompanied by both parents without additional documentation, we highly recommend you travel with the following documentation:

Many countries require documentary evidence of the traveling adults' relationship to the child and permission of the parent(s) or legal guardian before they will allow the child to cross the border. Single parents, grandparents or guardians traveling with children often need proof of custody or notarized letters from the other parent authorizing travel. These requirements are in addition to passport or proof of citizenship requirements.

* Minor traveling with one parent: If a minor child is traveling with only one parent, the absent parent is recommended to provide notarized consent. If only one parent has legal custody, that parent should be prepared to provide a court order of child custody to airlines and international authorities.
* Minor traveling alone: If a minor child is traveling alone or in someone else's company, both parents (or the sole, documented custodial parent) are recommended to provide notarized consent.
* Minor with a different last name: If a child traveling has a different last name from the mother and/or father, the parents should be prepared to provide evidence to airlines and official authorities, such as a birth certificate or adoption decree, to prove that they are the parents.
* Minor has one deceased parent: If one parent is deceased, a death certificate should be readily provided by the other parent.
* Minor has one parent: If the birth certificate shows that the minor only has one parent, it will be sufficient to hold only a notarized copy of the birth certificate.

I would like to add one thing to Frank's post. Any requirement for a notarized copy of a birth certificate is misleading. No official document can be notarized. If you need a copy of birth certificate, you should get a certified copy from the issuing agency.

In addition, you should probably have her parents provide you with their authorization to give consent for medical treatment for her. You'll probably want to consult with an attorney for the proper forms.

You should probably ask this question directly to the embassies of the countries you plan to visit. Check their websites, most European countries have email help-lines on the Washington embassy sites.

Depending on the documents you need, you may have to use your state's apostille service. Basically, in order for a valid, official document (like a marriage lisence or birth certificate, for example) issued in one country to be considered valid in another, an apostille office must authenticate the document. The US government doesn't have a federal apostille office, but each state has their own.