You're more likely to get someone flexible and a bit cheaper if you go to a university or music college, as the students will often teach outside college hours and won't be as pricy. Get a personal recommendation if you can, always best.
If not possible, a music shop is a good place to start as they usually have registers of teachers. Qualifications are of course reassuring, but there are also many great teachers without letters after their names, so don't be put off. Ask how many pupils they have and how long they have been teaching, much more important than a shiny certificate.
Get the teacher to meet with your dd and see how they get on. Ask how they structure their lessons, do they have lots of "play" learning, colouring in etc or is it straight from a step by step book? This keeps it interesting for younger learners. Ask them how they plan to keep the lessons fun!
Ask what their approach is to the grading exams - I would be wary of teachers who are too exam orientated and want to notch up the certificates as fast as possible as it suggests they don't leave much time in between for actually enjoying the instrument. But do also ask how other pupils are doing, how well they do in exams etc.
Ask what their own preferences are - classical/jazz/contemporary/blues/improvisation etc etc and get them to play for you. If they seem to really enjoy themselves when they play their enthusiasm will rub off on your child.
Ask if they have other pupils in the area and do they ever arrange for them to play together, go to concerts, play their own mini concerts for parents etc.
Good luck, hope you find a good one and hope your dd enjoys herself!