The file name is actually going to be $(ProjectName).Publish.xml, and should be in the same folder as your .csproj file. If you enable the “Show All Files” option in Solution Explorer it will appear, and you can include it in your project from there. That will get it into source control.
One thing to be careful of: VS won’t auto-check-out this file if you attempt to change and save the profile settings, but it won’t throw an error either. There’s a warning in one of the Output windows about it, if you pay attention; otherwise it will just look like it’s ignoring your changes.