I had already downloaded the Azure PowerShell modules a while back, and I noticed that the documentation listed parameters that were not available in my cmdlets. The Azure Cmdlet Reference page states
Azure modules are updated frequently. If you notice that the online cmdlet help includes cmdlets or parameters that are not in your module, download and install the latest version of the module. To find the version of your module, type: (Get-Module <ModuleName>).Version
I shortened the command ('cause it's cool, but not always) and got the following.
Then I noticed that the same page referenced a version 0.8.0 of the modules, so I knew I was at least one minor version out of date. I then went through the install process for the Azure PowerShell Modules using the Microsoft Web Platform Installer.
Afterwards I fired up the Azure Console again and got this version.
So problem solved for now, but I needed to know where to look for an updated release notes page so that I could compare my version to the latest published version. This should have been easier, but I eventually found that we maintain a page for the Azure SDK Tools on GitHub and there is a handy ChangeLog.txt file there specifically for the Azure PowerShell modules.