If it's just a couple of hours of childcare, I'm surprised you've had any interest from anyone as it's not going to give someone that much income. Mind you, you haven't said exactly the hours you are offering.
What do I need to ask them?
Ask them about themselves, about what they have been doing over the years, what their childcare experience is, their general education perhaps. Find out the practical things, what would they be doing before they care for your child... thus how likely do you feel they may be late in picking up, also would they be available during pre-school holidays? Do they drive, if you need a driver that is an important question and you may well also want to know more about the car, suitable seats, suitable insurance.
CRB check?
If they regularly work with children they may well have one but it may well be several years old. Consider if this document actually tells you anything useful. It tells you convictions and cautions. If you read one, would you know which convictions and cautions would mean they are unsuitable to care for a child? It won't say on a CRB check that someone is suitable to care for children. If they do have one, how old are you prepared to accept. It's only valid on the day of issue, after that it's old. They could commit a crime the next day and you would be none the wiser - as parents can't check, parents don't get updates.
Just consider how important you feel that factor is... sure it may give peace of mind but it's possibly a false sense of security. Use your own judgement, look at everything to build up the big picture - do the references check out, does the person come across as genuine, do you like them, does your child like them, if they have a CRB check is there anything on there that they were not prepared to talk about.
References?
Follow up with as many as is practical ideally by phone. Again look at the big picture, do they have lots of written references going back many years and a couple of people you can call for a verbal reference. Are they currently in work, why did they leave their last job.
I am assuming they are not going to be registered in the same way that childminders are?
No, nannies do not need to be registered at all. In England nannies can optionally register with Ofsted - a benefit of that is that Ofsted then do a CRB check which supposedly Ofsted get told of updates (though never issue the childcarer with an updated check), so if a nanny is registered with Ofsted then they are considered to be suitable to work with children from the point of view of criminal background check. Being registered does not mean a nanny knows one end of a child from the other as the registration training requirements are minimal (could just do a Common Core compliant short course).
Nannies are registered usually because someone wants to pay them using Childcare Vouchers or Tax Credits. Whereas Childminders are registered because they legally have to be registered and undergo inspections of their home environment.
What is the minimum that I should be looking for?
Entirely up to you. Consider who you would currently allow to be with your daughter - what experience do they have? Your own mum for example... may have no formal childcare experience but did raise you and siblings. You may find that someone applies who has their own children or grandchildren and who isn't formally trained. Life experiences can count for a lot though you may want them to have some formal training as well.
Just have to take the chance?
Tune into your gut feeling. If something does not seem right, then be cautious. If something is telling you all is fine, then trust that feeling and do some more checking of things that you can check such as work history, references, their ID documents (do they seem to be who they claim to be?).
Something you need consider is if you want to be an Employer or not.
With a Childminder, you are a service user.
With a nanny, you are an employer. HMRC: PAYE Introduction will come in handy, as you will be doing Payroll.