Net pay agreement opens you up to unknown costs, you simply do not know how much it will cost you. So work out a gross pay rate that you can afford to pay and offer that. The nanny can then work out their Net pay from that gross dependent on their individual financial situation.
With a before and after school job you need to consider what happens during school holidays. Maybe you simply want just the weeks at school. So lets say that is 38 weeks and that you want 5 hours per day, so 25 hours per week.
(38 weeks x 25 hours)+ 12.07% for paid holiday to be taken during school holidays = 1064.67 hours. Lets call it 1065 hours.
1065 hours x £12 net = £12,780 net.
So we KNOW this is over the threshold for auto-enrolment pension (£10,000) and is over a typical single persons personal tax allowance (£12,500).
On that basis if you were to offer £13.25 gross per hour then I don't think it would be far different, for 2019/20 tax year if someone has full personal tax allowance of £12,500 and if pension was done using Qualifying Earnings calculation method at 4% employee (+tax relief) pension contribution.
Your cost would then be a little under £15,500 (just under £300 per week/52 weeks). I expect this is quite a lot more than you were paying your childminder.
As Popskipiekin has written, you can get help from a nanny payroll provider (they have online calculators to give you a guide) who you can call to get a more accurate cost estimate. They have software which will do what I just did above but with more accuracy. You need to determine how you will be do holiday entitlement, if your nanny needs to work at all during school holidays, if pay will be spread over a year or just paid for working weeks, that kind of thing as it will affect the calculations.
Personally I would pick a gross pay amount and tell candidates that is what you are offering. £13-£14 gross per hour may well be the sort of salary you need to pay in your area for before/after school care.