It's a bit weird to call your review of code a peer review if you're QA and not a peer developer. Not that I wouldn't welcome you at the peer review table so long as you act like a peer and review all the code, not just the tests. Heck forget the table, you can come sit by my monitor so we can fix things fast.
Don't limit yourself to just peer reviewing the tests or the code. One of the best things you can do is look at the code, the requirements, and the current tests and add your own tests. If you've spotted an issue that needs fixing writing tests is sometimes the best way to explain the problem. I wouldn't consider doing that stepping on my toes.
Indeed this is a way I'm used to working. Having that kind of hands on QA lets me go fast because I know you've got my back. Be sure your shop feels the same way.
One thing I beg you not to do is create a pile of manual test documents. As that pile gets taller and taller releases get delayed longer and longer. If you do create a manual test get it automated as soon as you can.