In terms of making the PI happy, disclosing is the only way to go. If I were the PI, I would want the start date to be after the delivery and any maternity leave. That arrangement is obviously going to be in the self-interest of most PIs given the parameters that you list.
... unless the PI wants her to be in the lab in the winter so that she can get some training.
Does she know with certainty that the postdoc cannot be yanked if she discloses the pregnancy? (Yes, it's illegal; that's not what I mean.)
If the pregnancy is a deal-breaker for her new PI, she should move on and find a different one. The PI is going to be writing her recommendation letters. Anyone who
would revoke the opportunity surely won't write complementary letters if he or she feels "tricked" into taking on a pregnant postdoc.
If she really is flexible about the start date, she should disclose the information.