Email alerts (dock icon and app sidebar) arent showing up in any more in 10.9
Mail.app in 10.9 has had (and still have, for some) massive problems with Gmail-based accounts.

In the first couple of Developer Previews Mail.app was completely unusable for me. When the Golden Master (final release) of 10.9 came out it was better but still horrible compared to earlier versions of OS X. In my case, Mail did actually show the unread badge, it just showed a number was way off!

Try to update OS X to 10.9.1 which makes Gmail-based accounts work better. Also, there was a stand-alone Mail Update for Mavericks which fixed the badge problem for my.

You probably know but it's through the App Store or Apple menu () > Software Update.