Exactly what the title says; what if Caesar Augustus had a son by his wife Livia?
Alternately, I suppose, his daughter Julia could be a boy, but she was a character, I'd rather keep her as she is.
I am afraid the Julio-Claudian-Dynasty would nevertheless not stop to kill heirs as soon as possible and finally die out.
Without Tiberius, the early principate would perhaps become less relaxed and peaceful.
Without Caligula people would not get used that fast to autocracy and
without Claudius the empire would miss one of its greatest reformers, with some serious consequences.
Well, if an other emperor than Caligula and Claudius would focus on Germania and ignores Britannia for now, thats another story.
A less experienced general than Tiberius might also come to a different and more appropriate strategy in Germania after 9 AD. Or at least does not let young Germanicus start this desastrous approach.
But other than that, I don't expect a significant change in history. Of course the Roman empire might still exist today, just because Augustus had an other successor. Butterflies sometimes cause storms, you know?