With a level 3 and a couple of years experience, she could apply for jobs on cruise lines or holiday companies. Sometimes the owners of private villas will hire a nanny to live at a property full time to take care of the children of different families who hire it.
TEFL is always useful. If she really wants to work overseas, perhaps some other basic language courses (Russian, Arabic, Chinese) would be helpful for her?
Does she read any of the sector magazines, like Nursery World or Early Years Educator? (They're all available in WHSmiths) Apart from keeping her up to date on what is going on in the sector (really important right now, given the changes the government keeps making), they also have job adverts at the back, often for companies like Disney Cruise Lines, which might help her to get an understanding of her options and what they would be looking for. (Most of them are looking for something along the lines of 'L3 qualification and at least 2 years experience, or similar, so having done a 2 year apprenticeship she may well be eligible). The Lady magazine is the legendary one for nannies and mother's helps, etc (and sometimes has overseas nanny jobs advertised).
I wouldn't go for au-pairing if she has qualifications and wants to do childcare as a career, as they are meant to be in a country to learn the language and culture, with childcare and light housework as a side duty to help earn their keep.
I think it's a bit of a 'horses for courses' situation between childminders and nannies, tbh. (I'm a childminder)
Childminders work from home, so you obviously have to actually have somewhere to work from, whereas nannies work in the family's home (though the nanny might well live out somewhere else).
Nannies work the hours set out in their contract with the family, and childminders set their own hours. The hours a nanny works might be quite antisocial, especially if the family mainly want evening childcare. But then a childminder might chose to work later into the evening and even offer overnight care (like I do). But then again I usually charge more for this, because it's outside of 'normal' working hours, whereas for a nanny it would just be their regular contracted hours.
In terms of wages, childminders are self employed, so set their own fees, whereas nannies are employed by the family and will be paid whatever the family has set as the wage. It means that childminders pay their own tax though, whereas nannies are part of the PAYE scheme (useful if you don't like doing tax, because god knows it a faff)
Nannies don't have to follow the EYFS, or be registered with Ofsted (though some will, on the voluntary register), whereas childminders, on top of actually looking after the child, then have to sit down and find time to do their planning (general and for each child), fill in each child's learning journal, fill in any forms (accident, injury, medication, etc), and then find the time to do their business paperwork! That said, having done the L2 and moving on to the L3, your daughter should be well aware of all of this! 