Possibly awarding Cameron Mitchell the Congressional Medal of Honor
In Season 9, episode 1 "Avalon", we see Cameron Mitchell flying during the Battle of Antarctica (previously seen in Season 7's finale "Lost City, Part 2"). After crashing, he has several hazy memories of being in a hospital.
The first one involves his mother at the hospital while it is decorated for Christmas (indicating that the Battle of Antarctica took place in December*). He also has two more memories of a doctor talking with him as well as Daniel Jackson, both of which happened while Christmas decorations are up.
But his next memory is when the hospital was no longer decorated for Christmas, indicating January or later. In this memory, Carter and two other other air force personnel are in full dress.
Carter: The Congressional Medal of Honor is the highest award for valor in action against an enemy force that can be bestowed upon an individual serving in the Armed Services of the United States of America. On behalf of the President…
Unfortunately, it's too blurry to see if Carter has the rank of lieutenant colonel on her dress uniform (which she was promoted to in the Season 8 premiere "New Order").
I'm inclined to think that the Congressional Medal of Honor was awarded in January, instead of a later month, because Mitchell's memories are still hazy, suggesting that he has not had much time to recover from his memories.
Putting this all together, Daniel Jackson visited Cameron Mitchell in December and then in January, Carter gave him the Congressional Medal of Honor. Since "Rising, Part 1" seems to take place shortly after "New Order", my best guess is that Carter left the base to give Cameron Mitchell his award during these events.
The other possibility, which I have no support for, is that Carter was helping at Area 51, as she was during the first episodes of Season 9. Sam's technical expertise would have been invaluable for helping to repair the ships damaged in the Battle of Antarctica, and with the possibility of more Goa'uld attacking, I could imagine an "all hands on deck" situation there.
* This doesn't line up with the episode before the "Lost City" two-parter, "Inauguration", in which a new US president enters office, because that happens on January 20th after each election.