Really the part that seals her death is that she told Cloud where she was going, which tipped Sephiroth off. She never intended him to follow, so it probably would have been better to just leave it as "bbs, on quest, ttyl". Thinking about it, it might have still ended in her death to take others with her, even if Cloud were left behind--because someone could let it slip to Cloud where they were headed and Sephiroth would have done the same thing, except instead of toying with the person on the pillar he doesn't screw around and starts the stabbing faster. So maybe she was actually playing it safe (in relation to not leaking plans, anyway) up until she sends Cloud the dream, because again, whoops! Doom sealed. Maybe she mistakenly believed she'd built up enough of a head start for it to not be a problem.
Her wandering into the Sleeping Forest alone and hiking to a Temple of Ancients that NONE of them even KNEW of before this quest while Shin-Ra is on their asses and a madman is wandering around like a loon is FUCKING STUPID.
lol no but really, as much as you'd like to scream otherwise, Aeris is not stupid. This is the same chick that runs around the slums like she owns the place, comes up with the plan to rescue Tifa, and has insight into Cloud's mental problems with very little to go on. There's really nothing to suggest she's an idiot aside from your own personal bias against the character.
I think it's pretty obvious she knew Sephiroth was after her -- yes, she was being led to the city by her heritage, but the guy had just tried to kill her via Cloud, I'M PRETTY SURE A LIGHT WENT ON SOMEWHERE.
And like Crack said, Aeris is not the type of person to put others in danger. Splitting the team up is a pretty stupid move because then Sephiroth could have just picked them off easier (possibly aided by PsychoSleeperAgent!Cloud). They simply didn't have the strength at the time to beat him -- and that still wouldn't have solved the problem of Meteor. The point is, she knew what she was doing was dangerous, and why would she risk the lives of the entire team when it was a mission that really, only she could do?