This is a question we get frequently. The fact that you are pregnant with the child of a US citizen while you’re awaiting a K1 visa doesn’t have any affect on your visa’s timeline or process. The fact that you are having a child together may help in terms of evidence that your relationship is bona fide, but will not expedite the processing. The reason it may help with establishment of “bona fide” is that if you were just doing this for the visa, it’s highly unlikely that you’d go through the lengths of having a child together.
The child in question would be automatically eligible for US citizenship, as the US citizen parent passes that citizenship down. Therefore if the child is born prior to entering the US, you would not file for a K2 visa as the child is already a citizen and citizens don’t need visas to enter their own country. You would instead file for a consular report of birth abroad, and get the child a U.S. passport. There is the possibility you will be requested to take a DNA test to confirm the child does in fact belong to the US citizen. If this is requested, you have no choice but to take it.
Lately, the consular officers have been requesting a sworn affidavit from the U.S. sponsor recognizing the pregnancy. It’s a good idea if you are pregnant during your interview to have this sworn statement from the US petitioner on hand in case it is requested of you.