Is there a token for the body of a content type?
There is a feature request opened for the Token module: Token for body of node.   Essentially, the reason it has not been implemented is performance issues, as modules are queried for the values of the tokens they implement, independently from the fact those tokens have been requested. This means the content for, e.g., [body] would be generated even if the string passed to Token doesn't contain that tag.
The Drupal 7 code that handles tokens is changed, and the modules that implement tokens gets the list of tokens that need to be replaced; the content of tokens that are expensive to generate is generated only when required.

In short, the only module that could implement that kind of token is the Token module, but so far it doesn't implement it for implementation issues. Any other module that implements it would have the same performance issues.