Actually, everyone could still have one child each. Each successive generation would be 1/2 the size of the previous and the population would approach a limit of approximately two times what it currently is since 1 + 1/2 + 1/4 + 1/8... = 2.
Immortality is generally taken to imply eternal youth as well (at least moderate youth). Not a lot of people want to live forever in a body that continues to age. Given eternal youth, there's no reason an 18-year old would be restricted to dating other 18-year olds. They could just as easily date 1000-year olds (unless by monogamy you mean eternal pairing).
