Keep the size the same as the camera defaults when shooting.
From the Settings > advanced settings window select the overlay tab.
In the TV safe zone, set the aspect ratio to 16:9
From the view menu, select "mask to safe zone". This will let you see the image as it will be finally output.
When you go to export your animation, from the File > Make Movie window,
Select (in the Size part of the dialog box):
Use TV safe aspect ratio
change the size to 1920 x 1080,
Crop to size
This will export in the correct format.