Or, they were waiting to make sure that the child was going to be a boy and not a girl so they'd know they hadn't wasted their time for all those months since they had already sent a fellow Knight to protect the other Royals (he was a brother of one of the dead KG, IIRC).
I'm wondering what they would've done when the child had been born. They'd be fools to think they could just raise another army around a baby, or that anyone would've recognized him as a legitimate child without proof. My guess is that once the baby was born they'd have taken him to Essos to be with Viserys and the Queen (not knowing she was dead).
It was a bad idea to hide in Dorne as well, because if anyone was going to be offended by what Rhaegar did as much as Robert and Ned, it was going to be the Martells. His selfishness cost the lives of Elia and her children.