"The baby is being born." is probably what you mean. Also, when a baby is "born," the event is called "the birth of the baby." Before a baby is born, when it is still inside the mother, she can feel it moving inside. The first movements are felt about 3 or 4 months after conception. This is called "quickening." When the baby is still inside the mother, it is called a "fetus." "The fetus quickens." "Quick" usually means "fast" or "speedy" but this is a very old and special use of the word.

Hi Elisa - that is correct!