Most of us (or at least many) holidayed with frienda of our own age at 17.
Who was responsible then? Genuine question, OP. Or do you not think 17 year olds should be allowed to holiday on their own?
Can you tell us, please, what you believe "responsible for her" will mean in practice.
If you can give examples of the situations you invisage which will require this, we can tell you what we think should happen.
This nebulous "responsibility" seems a strange concept.
For example, are you imagining her wanting to drink, and you not wanting to allow her?
I think in that case you need to back off and accept that as a girl saying a 19 year old, she is likely to choose to drink if she wants to. But if she is becoming problematically shit-faced/off her tits on drugs, speak to her about it, and to her friends)family if she won't listen. But I'd say the same for a young person of 19 or 21 to be honest - I wouldn't calmly stand back and let someone harm themselves on holiday with me whatever their age.....
Same with any worrying situation. Intervene only when there is a moral necessity to do so - age makes little difference.