I used to work in retail and had paid trips abroad. I would be paid for the entire length of the time I was away from home. I would get all expenses paid, such as all regular meals, except for minor top-up things like chocolate.
I don't see what you are proposing as being any different to a business trip... you are wanting someone to leave their home and be with you for a week (possibly more depending on travel arrangements). There will be times during that business trip that they are working and times when they are free to relax, do as they like. The salary may reflect a bit on how much freetime there is but not to a large extent, as they are still away from home and very limited in what they can. It's not a holiday for them... they are there to work.
What sort of hours would you say are reasonable to ask of her, in terms of help per day.
Anything is possible but I would focus on the times you need the most help. That may mean that their working day starts early afternoon and finishes early evening... so they can accompany you on an afternoon trip and provide evening care.
What sort of things would you want them doing? They are in a foreign country, they won't know what to do there and may have limited resources - so you will need to plan with them about suitable activities, outings, that sort of thing.
And day off?
Yes, they should have time off... travel days are working days, so without any day off they could be working 7 days in a row or more.
As they are away from home, I would suggest that is a paid day off... normal salary. You could argue that it should be unpaid but you want this person to come with you, so you need to give them incentive to do so.
Should we pay her wages as well as pay for her to come?
Yes, all usual wages are due for all days including travel days. An out-of-country allowance may also be applicable, to help give incentive for them to come.
I was thinking 6 hours in the day. And babysitting 5 nights. And helping at the airport.
Babysitting 5 nights seems a bit extreme. Is that all the nights you would be away? Working say 1pm-9pm could work but doing say 9am-3pm then 7pm-9pm may not be so attractive. It depends on the person but you need to consider what they would be willing to do and plan it all well in advance (plus you all need to be prepared to adapt that plan once there, as things may not turn out the way you plan).
Do you currently employ this 1:1 helper? If not, then I am not sure how you would go about having them come with you, as their employer may not be happy about them taking the time off. If they took it as holiday from their job, then worked for you, it's not really them taking holiday. They would need to be happy with the situation... they may prefer to be on holiday themselves, than to work whilst on holiday from their job.