Both are correct. But if you are trying to say that she walked from one side of the road to the other, then "across" is the best choice.

They're both grammatically correct, but only the first one has a clear meaning. The second one would be clearer if you said she walked "along the road" or "down the road."

As an American, I would never use 'over' to mean 'across'. 'over' would imply being above the road, for example taking a pedestrian overpass.

Usually we say ACROSS because we want to cross the road and get to the other side. There are a lot of CHICKEN jokes: Why did the chicken cross the road? (people think of all sorts of answers to this! Some a quite funny). But grammatically OVER is correct too. "I went over/across the road to see my friend. She lives over/across the road." Here's a sentence from The Guardian newspaper: Bernard Anonier, a retired cereal farmer lives over the road and Pierre-Alain Petit, a factory worker, is nearby. guardian.co.uk