^First contact with the Dominion happened a few months before Voyager
was lost, so anyone with Starfleet should have known about them. Chakotay was with the Maquis, so that might explain why he didn't know anything.
As for the EMH, I suppose he would only have been programmed with knowledge of species he'd be expected to treat. The Federation's first experience with treating a Jem'Hadar solider came during "The Abandoned." Bashir treated the child who eventually grew into an adult and learned about his genetic enhancements and drug addiction. Depending on whether that information was classified, the Doctor may not have known anything related to the Dominion.