"On one's way" refers to travel, or a figurative journey:
"¢ He's on his way to Italy. (He's on the plane now, for example.)
"¢ She's on her way to being the president of the organization. She's very ambitious, and is, indeed, brilliant.
About an expected baby, you could say:
"¢ A baby is on the way! (A baby is figuratively in transit now.) We're expecting a baby/ boy/ girl in May.
In your sentence above, you could say:
"¢ The party is gone, fellow Hector, she is gone. She's pregnant. She's two months along.