Death on the Nile by Connie Willis. I read it in Connie Willis' anthology Time is the Fire. I think this is also the answer to Man wakes on plane to find he is actually dead and heading into the Egyptian afterlife.
This is a novella rather than a short story. It starts with the protagonist on an airplane to Cairo - the protagonist is a woman but I don't think we ever learn her name. Things are already a little strange. There is severe turbulence and the protagonist cannot see anything, not even the plane wing, when she looks out of the window.
The tour party disembark at Cairo airport but things get stranger. Although the pyramids are a long way from Cairo airport the party can see them and walk there. It is at this point the protagonist sees the baboon:
There is a flicker of movement ahead, between the pyramids, and I stop and shade my eyes against the glare to look at it, hoping it is a souvenir vendor, but I can’t see anything. We start walking again.
It flickers again, and this time I catch sight of it running, hunched over, its hands nearly touching the ground. It disappears behind the middle pyramid.
“I saw something,” I say, catching up to Zoe. “Some kind of animal. It looked like a baboon.”
The party decide to visit the tomb of Tutankhamun and in a dream like transition they find themselves on a boat on he Nile heading towards Luxor. On arrival the party decide to visit a tomb, but one by one the members of the party disappear until the protagonist is left alone.
The implication is that the plane was destroyed by a terrorist bomb. During severe turbulence the protagonist remarks (apparently as a joke):
“We’re all dead,” I say. “We were killed by Arab terrorists. We think we’re going to Cairo but we’re really going to heaven. Or hell.”
and in the tomb she thinks:
The people on the ship were killed by a bomb, like we were. I try to remember the moment it went off—Zoe reading out loud and then the sudden shock of light and decompression, the travel guide blown out of Zoe’s hands and Lissa falling through the blue air, but I can’t. Maybe it didn’t happen on the plane. Maybe the terrorists blew us up in the airport in Athens, while we were checking our luggage.
The story ends:
I close the book. “There’s no point in waiting for Zoe,” I say, looking past the luggage at the door to the next room. It is lower than the one I came through, and dark beyond. “She’s obviously gone on to the Hall of Judgment.”
I walk over to the door, holding the book against my chest. There are stone steps leading down. I can see the top one in the dim light from the burial chamber. It is steep and very narrow.
I toy briefly with the idea that it will not be so bad after all, that I am dreading it like the clergyman, and it will turn out to be not judgment but someone I know, a smiling bishop in a white suit, and mercy is not a modern refinement after all.
“I have not murdered another,” I say, and my voice does not echo. “I have not committed adultery.”
I take hold of the doorjamb with one hand so I won’t fall on the stairs. With the other I hold the book against me. “Get back, you evil ones,” I say. “Stay away. I adjure you in the name of Osiris and Poirot. My spells protect me. I know the way.”
And as you say, the last line of the story is:
I begin my descent