I would archive the project with the Premiere Elements 11 workspace's File Menu/Project Archiver using the Copy option (choice is Archive or Copy). In this way you are creating a folder with your project.prel assets which include copies of the media that went into that project.
Typically that is done for the whole project. The urgent matter is keeping the media that went into the project.prel connected to it, lest you end up with the nasty missing media situation.
You can selective export a portion of the Timeline to a file saved to the computer hard drive by using the gray tabs of the Work Area Bar to span just that segment and making sure that the export settings include "Share Work Area Bar Only".
Another thought might be to make a copy of your project.prel which includes only the edited section, then use the Project Archiver on that.
Please review and see if any of that works for you.
More details to follow if necessary.
Add on about your saving question...
When the project preset is set up by the program or you, the new project dialog must contain a fill in for Save In: The default for that Save In is Documents/Adobe Folder/Premiere Elements/11.0 (assuming Windows). So, when you close the project and you are asked whether or not you want ot save the project, the project is saved to the location designed in the new project dialog unless you or the program changed that. (See File Menu/New/Project to get an idea of this setup if you have been depending on the project to do all the project setting.)
When you use the Project Archiver it will tell you that the project must be saved before it goes into action. If you selected the Copy option, you can designate the save location for the Copied Folder that will be generated (Folder with contain the project.prel + its assets.) When you want to open the project, right click the project.prel in the Copied Folder, select Open With, then Premiere Elements 11.