Pregnant in Egypt

Sarah mentioned in her last post that Sarah would have been pregnant with Yitzchak when she and Avraham went down to Mitzrayim for the second time. What I don't understand is how Avimelech didn't know that Sarah was married to Avraham if she was pregnant. You could say that it was because it was before she was visibly pregnant, but travel then was not like it is today. You couldn't just go somewhere faraway for a few days. It's not like she could have become pregnant there because Avimelech married her and if she had gotten pregnant before, it would have been noticed before HaShem had to tell Avimelech that Avraham and Sarah were married. Just thinking about it now though, that could have been one of the reasons Avimelech did find out other than HaShem telling him. But then, Sarah and Avraham would have already known that Yitzchak was going to be born before the malachim came to tell them. Which brings me back to original point. There is no way that Sarah could have been pregnant from before they went into Mitztrayim to Avimelech until the malachim came to their tent (possibly in Avraham's dream) to tell them without it being noticed. She must have spent at least a month or two in Mitzrayim, then they had to go back home, and get everything at least semi normal before the malachim would come. If this situation makes sense to anyone, please feel free to explain.