It seems quite probable Janeway knew of the events of "The Jem'Hadar", since one would expect word of a Galaxy class ship being destroyed by some new power in the Gamma Quadrant to travel quickly through Starfleet.
The stardate of "Caretaker" takes place after "The Search", so the Defiant was apparently already assigned to DS9 at the time Voyager docked, so one would expect them to know why
this bad-ass warship had been assigned there. (Whether the Founders were common knowledge at this point is debatable).
(It should also be noted, however, that stardates across series don't always mesh. For example, "By Inferno's Light" has a lower stardate than "First Contact", even though the preceding "In Purgatory's Shadow" clearly referenced the "recent Borg attack" from that movie).
Apparently as late as the fourth season, neither Chakotay, nor the Doctor were familiar with the Dominion, though given their backgrounds, they may not have had reason to be informed.
I remember reading somewhere (possibly one of the official magazines) that the threat of the Dominion is one reason why Voyager didn't plot a course for the Gamma side of the Bajoran wormhole instead of the slightly-further Alpha Quadrant, though realistically, given the number of hostile aliens they had to fight off or outrun, they probably would've been no worse off.