My daughter is 6 yrs old and lives with me.
Her father has another child with a woman he does not live with.
When is it appropriate, if at all, that I tell my child about this baby?
There is no possibility of the children to meet anytime soon, because we live in different countries and although I travel with my daughter often, the other woman does not want them to meet. he issue is that I wouldn't want my daughter to find out through anyone else, other than me. And pictures of this baby are on her father's Facebook page. We have several friends in common.....
How to deal, please?
The time to tell is now. You've correctly analyzed the problem: you don't want her to find out from any source other than yourself and it sounds like there are reasonable risks that that could happen. She's also old enough to understand the concept of family.
Be truthful but simple. For instance, "Your father has two families, and in the other family, there is a new baby. That baby is your half brother/sister. They live far away, so we may never meet them but maybe sometime we can see pictures."
A child this age does not need details and definitely does not need your judgment around this event. Keep your tone matter-of-fact. Ask her if she has any questions and answer them honestly and in age appropriate language that she will understand. If you don't know how to answer a question, tell her, "Hmm, I'm not sure. Let me think about that and get back to." When you figure out what you want to say, preface it by saying, "Remember you were asking me about X. Well, here's the answer......"
Expect that the topic may come up now and again, out of the blue. Be patient each time, even if she's asking the same thing over again. Children process information differently than we do and as new cognitive equipment kicks in in the brain, they are able to understand old information in new ways and that's typically what triggers the questions.
This is a matter of trust between your daughter and you. You want her to know she can trust the information you give her as being true and real. You want her to know you aren't afraid to talk about something that is complicated and difficult. She may not recognize these attributes now, but she will come to recognize them as she gets older and reaches different stages of development.