I think it is completely plausible Starfleet would keep information on the Dominion or indeed its very existence on a need-to-know basis. The wormhole itself is already something of a restricted-access asset to the Federation, an operation only slightly less secretive than Stargate. Knowledge of what lies beyond is a valuable card in the political game, and is not carelessly given away.
Chakotay was out of the Starfleet loop pretty early on, and wouldn't have direct knowledge as such. And he would have tunnel vision anyway: the galaxy is teeming with powerful potential enemies and allies, but very little of it touches the lives of the Maquis or indeed those of UFP citizens. Sure, the loss of the Odyssey would have made news back in its day (a couple of months before "Caretaker") - but there would have been more news the following week, possibly more spectacular, almost certainly equally irrelevant to the Maquis cause.
Remember, after all, that the Maquis mainly operated in the Demilitarized Zone. And that Zone was not in the immediate vicinity of DS9 or Bajor. Indeed, Bajor itself was removed from the Cardassian sphere of influence at that time, and the threats and opportunities that concerned Bajor did not necessarily have an impact on Cardassia or the DMZ, hence not on the Maquis, either.
Sure, Chakotay and Eddington and Hudson et al. would have been somewhat interested in the latest news on exotic threats like the Dominion or the Borg. But they'd have plenty to think already, and no way of knowing that the political entity that destroyed the Odyssey would in the future display an interest in Cardassia or the lowly Maquis.
Remember also that Chakotay wasn't one to see the Federation or Starfleet as his enemy. His angle was hitting at the Cardassians while following the Starfleet Way. He would take no delight in losses suffered by Starfleet.
Frankly, the Dominion just wasn't that big a deal at the time of "Caretaker" yet. Not even as far as Starfleet knew, let alone as far as the public was let to know.
As for whether Janeway would have been aware of the Dominion... Sure. There's nothing to indicate that she wasn't. But she wouldn't have any incentive to share that knowledge with Chakotay until it somehow became relevant for their Delta Quadrant predicament. It's not as if she felt an obligation to discuss any other aspect of recent Starfleet operations with Chakotay, either - not even the anti-Maquis campaign!
Certainly there would have been extremely little reason to assume the Dominion was in any way related to strange happenings in the Badlands. Janeway might just as well have been preparing against an encounter with the Borg in there! (Actually, her best bet at the time would probably have been Klingons, who had an old battleaxe to grind with Cardassia, or perhaps Romulans intent on framing the Klingons.)
Timo Saloniemi