Safety kampala (Kampala)

Hi :-)
My family and I might be moving to Kampala and as we have a small daugther, I have some questions in relation to that.
We will be living in Kololo I think. Where I come from safety is not a matter - and I go with the stroller everyday, and also run/jogging. Is that at possible in Kampala /areas like Kololo? Would it be safe?? Especially I would find it hard to miss walking with my baby daugther, as she is only 1 year and love to be walked with :)
And Health - are there good doctors? My husband Will be Working for an embassy, whom am sure will help us, but I have so many questions allready...
Thanks
Best regards
Laura