I am going to add this as an answer, but it's only a partial one.
Depending on age and other factors your daughter may qualify for "unsupervised minor" treatment. The programs vary a lot depending on age and needs, and it's up to you and the airline to work out the details, but essentially it falls into two categories.
If she is "very young" then she wears a sticker and is assigned a "guardian" from the airline. This flight attendant (usually) will stick with her the entire length of the flight, will give her special attention, will help her though customs and any security checkpoints, and so on. This is basically a baby sitter. On connecting flight they walk the child through the airport and all security "stuff" to their connecting flight. They may hand off the child to a flight attendant on the next leg of the trip.
If she is "young" then she wears a sticker, and special accommodations are made (these apply to very young as well). Most notably she is put on a list and the connecting flights are not allowed to leave without her. Her seat can't be "bumped" and if she gets "stuck" in security the plane has to wait. The security and immigration/customs etc. people are aware of the sticker's meaning and will go out of their way to make the process smooth for her.
It may be worth while (especially if she is under 18) to speak with the airline about these programs. Usually they are called "Unaccompanied minor" or "Young Traveler" programs. Signing up for these will also let you bypass security and pick her up at the terminal, instead of having to wait at the airport exit/baggage claim.
Now, I am saying all this, but make the realization that these programs started "back in a time" when minors traveling on an airplane alone was no big deal. I remember using these when I was as young as 6 or 7. These days people are likely to scream bloody murder if you have a 6 or 7 year old travel alone. Because of that these programs are not as popular as they once were. Also international flights are a bit different then domestic flights and I realize that, but don't be afraid to use these programs. You may be met with a bit of "Oh my god, I can't believe that a parent would let a child travel alone! What a horrible parent." Just power through that nonsense and talk with the airline. They do have a plan and system in place for these types of things, and they really are good at it.
Be aware that there is a cut off for non-direct flights, and there is usually a fee. Unaccompanied minor status is usually valid till they are 18 upon request and usually a requirement until they are 16.
There are some restrictions depending on airline. For example: