All I really want the nanny to do is look after the children, so not asking for simple housework to be done. I will have organised food already for the day. Just ask she cleans up after them and gives them snacks etc.
Not sure that is really a good idea. It creates a lot of work for you and does not give the nanny much to do... they may get a bit bored. Also things will change over time. Currently your DD is 9 months, so food is quite easy. In a years time she will be eating more and it would be nice for nanny and your DD to be eating the same thing, so your DD gets to copy an adult eating.
I live in Hertfordshire and was thinking about £7:50 an hour before tax?
Do you mean £7.50 Gross (before tax deductions)? If so then that's a bit low I think for a qualified, experienced nanny. It may be possible to find someone who has just left college, or in say their 2nd nanny job. But if you want someone with baby experience then you may need to offer more than that.
However, it is a figure you have come up with so I guess it is what the budget is, so advertise the job and see what applicants you get. You need to keep in mind things like annual reviews, activities costs, travel on duty costs, so the salary may change over time.
How do I set up all the tax, NI for them? I will be doing this myself and although read some threads on here am still confused.
As it's your first time, I suggest using a payroll agency such as www.payefornannies.co.uk who will sort if out for you (fee is around £125 a year). Once you get a bit more used to it, you could stop using them and produce payslips yourself using info from HMRC.
Also my other problem is, although I start in April I only work for 12 days and have the rest of April off. What do I do about this?
Nannies are paid all year round generally. So you could see if nanny could take some of their holiday entitlement, especially if some of those days you are not working are over Easter.
I don't really want to be in the house but can't always make myself scares and can't really ask her to not work.
Nannies are used to having employers around at home from time to time. Your DD however may find it a lot harder as she is at typical separation anxiety age. Best to just go with the flow and spend time with your DD and also spend time on your own. Another reason for adding some household duties such as nanny helping with the washing.
Also how qualified should the nanny be? I want first aid trained and experience with babies ( DD will be 9 months) but do I need to think about anything else?
It is hard to know really. It's more about someone having common sense - which isn't taught on a course. First Aid training is important when working with babies, as they can stop breathing and can rapidly go downhill when ill. You want someone who will interact with your DD, who understands babies and also isn't afraid of toddlers - is used to dealing with toddler tantrums. These things often come down to Experience, rather than qualifications. So look more towards what experience a person has with babies and toddlers. Qualifications are useful however if you are able to use Childcare Vouchers or any other childcare funding scheme.
Do you need someone who drives? I think the answer to that is YES, because unless they live very near you and can walk - they will be needing to get to your home very early in the morning.