yes you can terminate the contract, as long as the reason isn't due to the pregnancy. Trouble in your case is that the reason is associated with the pregnancy, so you need to tread carefully. May well be worth getting some expert advice on the matter (your insurers may provide a free legal advice line). Also try posting in Legal section of Mumsnet, should any nice HR people be able to confirm things.
DWP: SMP Eligibility
SMP Dates Calculator
If you terminate your nannies contract before the qualifying week (week 15 before EWC), then I don't think you pay SMP.
See DWP: SMP Eligibility
"You will not normally qualify for SMP if your employment ends before the qualifying week. This is the 15th week before the week in which your baby is due."
Your current reason for choosing the nursery seems to me to be due to your nanny being pregnant.
You could perhaps choose a different reason, such as financial difficulties (nursery I presume would be cheaper for you).
It is tricky and a bit of a minefield... the dates may be quite important, as if employment is terminated before Week 15 before EWC, then right to SMP would not exist (in my view... do check yourself using the DWP guide with the dates you have been given).
HMRC: SMP Overview
HMRC E15 SMP Helpbook (PDF)