Hi Meca,
If the baby is born in the UK, then it is automatically a British citizen, therefore entitled to a British passport. As for when a baby is able to travel, I have read on certain websites that it can be from about 1 month old, but they do say to ask a doctor, just to make sure. I am only going on what I have read though, so maybe someone else can give you definate information about it.
Congratulations on the pregnancy too.