sounds like a nice little job for her and will give her some good experience.
I run babysitting course for girls aged 13-16yrs in my current job and we suggest an hrly rate of £2.50 an hr upto £5 an hr depending on age, exp and any additional quals they have such as first aid as thats not part of our course (we just do minor injuries).
so £4 an hr is plenty and very generous.
good luck with the new addition when he/she arrives.
I started babysitting when I was 12; it depends on the individual, if you've grown up helping with younger siblings etc then you're perfectly capable. I think I'd pay a little more for the extra work, £5?