How is nursery funded - are you paying for that, or is it free? What percentage award have you got for Childcare element of WTC?
With one child, if you had an 80% award, then max weekly amount is £140 (see WTC5).
I calculate that the nanny would be working 1300 hours per year, which if you managed to get them to agree to £6 per hour gross (which is above minimum wage, so could be above what they get at nursery), their salary would be £7800 gross per year. Employers NI on that is roughly £941 (source: E-Gismos UK PAYE calculator) so your childcare cost for WTC purposes is £8471. Max claim amount is £7280, so that will result in you having to find £1461. This does not include any expenses the nanny may have, travel costs, the extra heating/light at your home, extra food etc. It is purely calculation based on salary alone.
I don't know how WTC works, in terms of how long it wakes them to sort out payments to you, but I would imagine that there may be delays on occasion, so you need to take account of paying your nanny from your own salary, then you live on the remainder of your salary plus the amount from Tax Credits when it turns up.
Not sure if that is of help or not. Without knowing a great deal about your finances, can't advise if it makes financial sense to do this or not... my gut feeling is that care for just one child can be obtained at a lower cost in many areas - for example, childminders in my area charge £4.50-£5 per hour.
I would suggest researching how much it would cost for your DD to attend nursery full-time (8-6), and also other forms of childcare such as registered childminders.