I think Elizabeth going after Will was primarily because she found out AFTER Will had already left that they were both still going to die. Will would find Jack, keep his part of the bargain, come back to Port Royal, and still be hung. She knows Will, knows that he will keep his promise, that he'll be back for her.
She HAD to find Will, because otherwise he would die. Perhaps a small part of her wanted to help Jack remain free, and I figure that both she and Will, once he knew what was going to happen, would have worked with Jack to figure out a way for all of them to be free and clear.
And there is no way she could hang out in Port Royal. Just about everyone knew who she was, and even if she disguised herself, she might still get caught, eventually. Better and safer to be on the move and find her fiance, and Jack. Strength in numbers and all that. 😄
I have a feeling that once she got to Tortuga, she would do exactly what Will had done; start asking around and seeing where she could find Jack. If she finds Jack, she finds Will. It's not a gutsy plan, per se. It's a smart plan.