Yes, you can send image (JPG only, if you shoot RAW then you can convert your RAW into JPG in camera) directly without the need for computer.
First you need to connect your 6D to the computer via USB cable (disable Wifi, if wifi is enable, USB port will not work).
Turn on EOS Utility software.
Configure camera settings to eenable access to web service.
Disconnect the cable, enable wifi
Now you can send photo directly.
Thanks HSBN. I've got it working. Although it was a struggle changing the settings through EOS to include web services, because I kept getting a message that Canon iMage Gateway wasn't available in my country (UK). But Canon's helpline sent me software to reload EOS Utility and then it worked
I presume on the 6D there's no way of just quckly using the wifi just to quickly email one or two photos you've just taken to someone straight from the camera to them?
I guess you first have to either get them on to some storage service like Canon Image Gateway or Flickr - or perhaps your own Image Browser or Digital Photo Professional - then sign in to that and email it. In which case I suppose you might as well download the images on to your computer, login in to your email account, and attach them and send them.