I have a child project's iteration that I want to share with the parent and peers. Do I just use the same iteration name and create at the parent or will this make duplicates on the children that already have the iteration created?
If you create an iteration in the parent project with the same name and dates then the information from the child child projects should roll up to it when you view it. You will need to enable the ability to view items from child projects if you haven't already though.
You will also want to make sure not to bulk create the iteration in the child projects. When you are creating the parent level iteration there is an option in the very lower right labeled Cascade. Set that to off. I think it would provide an error if you attempted it because there should already be iteration with same date in the child projects, but why risk it.
In the future you can create the iterations directly from the parent project and set Cascade to on so they will be created in the child projects at the same time.