If this happens a years before the first book, then yeah: Domeric survives.
In the grand scheme of things, that will not make a huge difference for Robb's actual campaign. He was said to be a decent fellow, and a great rider with the makings of a tourney champion. If he lives, that's one more capable lord upon whose service Robb can rely, so that's a plus. But does that change the course of the war? Nah. So the huge outcome remains the obvious one: no Red Wedding. Also: the Hound returns Arya to her family, hoping to be rewarded. He might be, at that. Robb wants to kick the Lannisters to the curb, the Mountain is in the employ of the Lannisters, so a nice reward for the Hound plus a promise that the Mountain is his to kill would probably get him in Robb's service.
Later on, instead of taking Sansa to the Vale, Littlefinger will presumably seek to return her as well, while concealing all his previous back-stabbing. Both in order to angle for Cat's gratitude, and to get in with the winning side. (Because short of the Red Wedding, Robb is pretty thoroughly beating the Lannister forces.)
However, per the OP, the actual idea is that there are no Boltons left. So if we take the "one year before AGoT" indication as a mere estimate, and conclude that "five months before the book" (just after Domeric dies) is equally acceptable and indeed yields the intended outcome... then all the above still stands, but Ned can use the extinction of the Bolton line to secure a decent future for his bastard son. This is then enough to prevent Jon from going to the Wall, and puts Jon at Robb's side during the war. (Taking the place of Domeric in the scenario above.)
This obviously changes the whole plot in the far North, with potentially world-ending consequences. Without Jon, Mance's plan goes through as planned. (In fact, the bulk of it has already happened prior to the moment that the Red Wedding was set to occur.) Blackwater has also happened. Without Jon at the Wall, do Melissandre's visions tell her the same? That is: does she convince Stanning to go to the Wall and intercede? Or do her visions instead tell him to join forces with the Starks or something? (And if so: does he listen?)
Things start getting pretty unpredictable at this point. But let's assume that Stannis still goes to the Wall, and still manages to fuck up Mance's plan. Let's also assume that the Wildlings are clear enough in expressing their fear of the Others, and that Mellisandre urges Stannis to take it seriously. No Jon Snow means Stannis presumably gets the unused castles along the wall to station his men. So now he's King-at-the-Wall.
Meanwhile, the Ironborn still raids Winterfell, but no Boltons, so the North is a huge mess. Theon now has to double down on his shitty choices, but we may assume he still doesn't kill Bran and Rickon.
I assume that, faced with the Lannisters and winning, Robb figures he can keep going down South, and then turn around to reclaim the North. Stopping the campaign to avenge his (supposedly dead) brothers would be a really stupid call, strategically. The Ironborn have no real hopes to hold Winterfell against him, so he can retake that whenever he wants. But his chance to beat the Lannisters is now. Presumably, he continues winning battles. Once Sansa is returned to him, the Lannisters have no hostages. By this point, there is little doubt that the Vale is, if not actively with Robb, at least not with the Lannisters. And Dorne hates them anyway. So it's the Lannisters and the Reach versus all the neighbours.
I sort of doubt whether Robb wants to conquer everything. Pushing on would be great from a "yay, vengeance" campaign, but no way most of his lords are going to be happy about that kind of thing. Plus, Joffrey and Tywin are both dead by this point. The 'Dornish marriage' plot may well have been averted due to the altered geopolitical realities, so Cercei still has Tommen and Myrcella, and thus: things she can lose. Everybody will be pressuring her to seek peace, and somebody like Kevan Lannister will certainly be pushing for it no matter what Cercei wants.
Robb's demands will probably boild down to: the North, the Vale and the Riverlands will be divorced from the Iron Throne, and will be independent states (presumably in a league of some sort). Dorne probably gets the same deal (but merely in a more loose alliance with the others). That, plus some sort of indemnity, presumably to be brokered via the Iron Bank to ensure future compliance.
After that, Robb can turn his forces back North, and drive the Ironborn out of Winterfell. This leaves him with the problem of Stannis still being holed up at the Wall (and the flood of messages about the undead besieging the place), as well as the question of whether or not to attempt a punitive campaign against the Ironborn.
I'd assume that by this point, we're somewhere in the second half of the year 300.
