As a travel agent I can tell you this much, you can leave the USA without a passport but you will not get back into the country without one. This applies to all travelers not just adults. And it is best to get the baby her/his own because then they can travel with either parent. Years ago they just added the baby to Mom or Dad's passport but then they had to always travel with that parent.
Getting a passport can take some time so if you want to travel this summer you need to get started now.