Hi,
You should be talking to your Doctor or a Travel Nurse.
However, for advice on anti-malarials for children have a read of the Health Protection Agency (UK Government sponsored) 'Guidelines for the prevention of malaria in travellers' website
http://www.hpa.org.uk/webc/HPAwebFile/HPAweb_C/1206520188455
and here is information about the different prophylactics and the dosage for people of different ages from the same source.
http://www.hpa.org.uk/webc/HPAwebFile/HPAweb_C/1206520188016
As for Yellow Fever if you are entering Kenya directly from Europe, North America, etc you will not be asked to show a YF certificate., you will need it if you travel between Kenya and other Sub-saharan countries.
There is virtually no risk of catching the disease, there has only ever been one outbreak in Kenya and the last case forum that was reported in the mid 1990s. Even the ultra-cautious WHO changed it's advice a couple of years ago and no longer recommends it for large areas of Kenya. In fact the Kenyan government in association with the WHO has just started an exercise to determine if kenya can be reclassified as low or no-risk.
Lots more info on Yellow fever here http://www.tripadvisor.co.uk/Travel-g294206-c151998/Kenya:Yellow.Fever.html