if you are not ready to make it public, do it on a need to know bases - if you feel sick/exhausted and you need help it's best to explain to those who help you - but ask them to keep it a secret till you tell DD!
I normally tell grandparents and some close friends first, as they are the ones whose help I tend to need with school runs etc when I'm sick (which I'm, a lot, every time).
they very good at not outing me, trusted circle of few!
then kids, then the world
people generally wait till 12 week scan, just in case something goes wrong, but when we had a MC (5th pregnancy) I was actually glad that people had known, I had a lot of support and I didn't have to suffer in silence/secret.
it was good that my boys knew what happened as well, made it a real bonding thing actually (they were just the sweetest...)
I didn't make pregnancy public with DS5 until after my 1st scan though - but I had an early one at 9 weeks so told kids straightaway!
DD - again I told everyone around 8 weeks, as soon as I was sure.
I wouldn't worry about the relatives, wait to tell DD - and make it special, I'd suggest having a bath together and eat some ice cream at the same time, she'll remember it forever!!