Well if you're going through Eden or another agency they (hopefully) will have vetted them throughly but things can slip through the cracks so you might want to ask when their last CRB (now known as DBS) check was done.
If you want to be a bit more formal or if the girl doesn't seem to have years of experience I'd ask what relevant qualifications or training they have. If she's an older duck with years of references it's not essential.
How many years newborn experience do you have? I'd not take anyone with under 5 to be honest. Again, coming from a good agency this shouldn't be a problem but some girls will say they've had newborn experience and when you dig a bit deeper it can sometimes be that they helped out Mum while looking after an older sibling.
How long have you been working as a maternity nurse?
Do you have paediatric first aid and when was it completed? (3 years ago is the longest you should accept)
Depending on your circumstances you should ask if she has the relevant experience. i.e., if you're planning or thinking you may have to have a c section ask her if she's had lots of experience with c section Mummies. Ask her also about working with jaundice, colic, reflux.
Depending on your feeding plans ask if she is willing to work with you through the night. She can help burp and change IF YOU WANT and can feed if you want to bottle feed. Check she's on the same page and supportive.
Most mat nurses love to swaddle. If you don't want to swaddle then this is something you should discuss at interview stage.
Routines. What are her/your feelings? Do you want to have a baby led routine, one of your choosing or leave it to her? If you want baby or you to lead, will she be ok with that?
Has she ever had an emergency and how did she deal with it? You can learn a lot with this question.
Will she be happy to do very light cleaning (if you want), make some simple meals for you and do baby laundry. Most will but a few snotty Marys might not be happy to. Best make sure first.
Make sure you're on the same page regarding going out. Most maternity nurses like to get out and get baby air every day.
Sleeping. Some like to sleep with baby, some like their own room. You may not even want an overnight but you'll be glad for it if you do!
What hours do you want her? Usually 24 hour slots although I've done just days and 24/7 also.
What happens if baby is late or early? What's her deposit? How and when does she want to be paid? Cancellation policy? You can ask about travel expenses. I know some expect them but I never did and it's always something they can bring up if they feel they want them.
Does she have her own contract? Most experienced mat nurses will.
Ask them why they choose to be a maternity nurse, what makes them a good mat nurse and what are their best and worse memories.
It looks daunting but the difference between an ok nurse that you sort of get on with or a wonderful nurse that you really gel with can make it a wonderful experience for you.
In quite a few of my positions I stayed on longer as asked, the longest one I was there for 5 years as I'd stay on for a year then they'd have another! Another I stayed in for two years. Most of the families I'm still in contact with to one degree or another, it's funny seeing their teenagers on my Facebook!