Is this a correct way to congratulate someone on their new child?
All that looks really fake, insincere and awkward. For a start, it repeats itself - which isn't good English. Title - Congratulations. (That's enough.) Headline - Many congratulations from all of us on the birth of your baby. (There's no need to say 'newborn'. All babies are newborn. No-one gives birth to an adult!) Why add 'our colleague'? She knows she's your colleague. Just say who it's from, but maybe say 'With love and best wishes from ...'? And at the bottom, 'We wish you and your baby (add 'son' or 'daughter' if you know which it is) a lifetime of happiness, joy and love.' That would be far more natural and less formal.
"the newborn" sounds quite odd, like it's some kind of object. We'd say "YOUR newborn (baby)".