It is a virus which is spread via droplets - so from breathing. In theory your nanny could catch it and could in theory pass it on. However there is a vaccine for this, so depending on the age of the other children, they may already have had the vaccine (it is usually given around 12-14 months of age).
As a childcarer coming into contact with childhood diseases is an occupational hazard. I would have thought that your nanny could ask their GP for a rubella immunity test (this is a test done for pregnant women) they may be charged for it, to confirm that they either have had the vaccine already, or if they need to have it. Your nanny depending on their age may have had the vaccine as a child. Up until 1996 (I think) rubella vaccine was given to girls at age 10 to 13 years. The MMR was introduced around 1988 and given to children around 1 year old and again at around 3 years old.
NHS Choices says: "Someone who has the rubella virus is infectious for one week before symptoms appear and for up to six days after the rash first starts."
So like other childhood diseases, it spreads before it shows symptoms, so assuming your nanny worked last week, then they have probably already been exposed to the virus.
I feel that the nanny should still work as the chances are that they have had the vaccine and that the children they care for have also had the vaccine or still have parental immunity. If it is convenient to you, then you could allow them to take annual leave, to try to ease the situation. If your child's symptoms get worse, then I feel you should consider staying at home with them as children who are ill want their mum usually, not their nanny.
Rubella is rare... NHS Choices says there were 12 cases in 2010 (England & Wales). Rubella is a Notifiable Disease so although symptoms are usually minor, it is a condition that the health authorities monitor.