Can Entity Translate work on the node body?
Ah turns out you have to enable translation for the field once you've enabled translation for the content type.

Open up your content type, edit the field you want to make translatable then head down to the bottom of the page.

You should see something like:

Field translation
Users may translate all occurrences of this field:


Body in Basic page
Body in Article
Body in Webform
Body in Test Content
Body in Upgrade &amp; Search Token Product Display
Body in Blog post/Article
Body in Development Blog


Click on "Enable translation" and you're good to go.