~.~.
My 8 year old son has traveled internationally with my dad. I did a power of attorney through Legal Zoom since I just needed something basic. You can grant full power or limit it to medical decisions, housing, etc and you can include an expiration date as well. I was not traveling with them, so I did limited control with an expiration date with my ability to revoke it at any time.
With you and your husband traveling, I would also make sure you have a will in place, just in case something happens to you on your side trip, that details out who will have custody of your daughter. Include in the power of attorney that upon your death, power would transfer to whoever would take custody of your daughter. Have copies of your health insurance information, passports, prescription information, etc. Keep a copy with you, a copy with someone at home, and a copy with the people you are staying with. You can register with the embassy when you get over there to give them your contact information, however it's usually not required if you are there less than a certain amount of time.
I wouldn't worry too much. The chances of something happening are slim.