You and your son could join him now but it would come out of your pockets.
It will take the navy anywhere between 2 weeks to a month to process the marriage itself so you start getting paid for it. However his #1 priority should be getting you and your son into DEERS so you can then be enrolled in TRICARE and have medical coverage for the 2 of you.
You should be able to join your new husband in a few weeks after he finds an area to live, gets everything set up for you and your son to arrive.
Congrats on the new marriage, the new baby, and the Sailor husband. You are going to have a wonderful time and it will be stressful sometimes but it is all worth it in the end.