Oh, they'll all be running. McCain, Huckabee, Allen, and probably half a dozen others (or more). Don't forget Pataki or Giuliani. If we're assuming a roughly similar 9/11 situation, one of them is certainly going to be on a ballot. True, the GOP has a primary system biased against moderates, but the whole point of 9/11 is that some things rise above partisanship. They're certainly top choices for the vice presidency, if not the top spot, especially Rudy.
Gore's got a fighting chance, for sure. Incumbents are hard to beat. People are rallying after 9/11. It's doubtful that the GOP will be able to make an effective anti-war narrative play with their base the way the Dems did IOTL.
But there are some things against him: unlike IOTL there's a clear narrative for the GOP on terrorism: "this is all the Democrats' fault." The setup came under Clinton/Gore, and the attack came under Gore himself. A lot of potential candidates will blow their chance to make hay of this by supporting the president at first- McCain will have problems, so will Allen, probably Pataki and maybe Giuliani. Huckabee probably comes out swinging hard as a guy who wasn't in congress when it all went down. Giuliani can possibly get out from under it by saying he only ever had time to focus on reacting. ITTL the GOP also has the advantage of (and pardon me for reducing this to pure politics) totally scapegoating Muslims. Bush, as president, as a person who needed to maintain alliances (and who honestly probably just had an ounce of character in this regard if I'm being charitable) couldn't just blame the Muslims. A GOP out of power looking to take it back in 2004 would likely have no compunction about going after Muslims.
I'd put the odds slightly in Gore's favor under these circumstances. Given an optimal GOP ticket like McCain/Giuliani he could lose pretty handily. Maybe a reverse of OTL's 3 million Bush win in 2004. But if conservatives subdue the moderates in the primaries and you get something like Huckabee/Kasich or even Allen/Huckabee, the edge is probably still with the incumbent. Say Gore by 2 million; closer than OTL but still solid.