Once I traveled to Puerto Rico, and the flights were considered domestic flights. I did not have to go through US immigration. The security on my return flight to the US however asked me casually if had a US visa (I had a valid F1 at that time), but did not check my passport. My guess is that if you have a previous visa and the new H1 approval, then you are fine. Post 911 it is better to carry all relevant travle documents even for domestic flights. Ask the airlines about the visa as well.