First of all, have GoDaddy change your plan from Windows hosting to Linux hosting! WP and other software of this type function much better in a Linux environment. Don't worry, you do not need to know anything about using Linux as the GD control panel looks after all that :) WP, and others, have "issues" when operating in a Windows environment; why complicate things :)
Once that is done, the GD auto install will absolutely be available to install to your web hosting root. Others may recommend installing in a sub directory, but as this involves extra steps, again, why complicate things, especially if this is going to be the only site hosted on the account.