Yes, the GAO exists. But under the current administration, it's basically like a security guard that just sits there and watches crooks do bad shit, reports it, and then nothing happens.
However, creating an agency in the legislative branch is another story. One of the duties of the legistive is to investigate the executive, is it not? (not that this matters when both the executive and legislative are controlled by the same party)
Aren't most of the inspectors general positions they fired still vacant?