To best mirror Eclipses functionality, enable the following settings:
To see the javadoc in the autocomplete menu, hit '.' to get the popup, then hover over the object you are working with, once you get the javadoc popup, you can select an item in the popup to switch the javadoc over. Not ideal... But its something.
As another note. The search functionality of the options menu is very useful. Just type in 'doc' and you will see all the options for doc.
Also, searching for "autopopup doc" will not only find each of the options, but it will also highlight them in the menu. Pretty awesome!
Edit: Going beyond the initial question, this might be useful for people who just want quick and easy access to the docs.
After using this for a few more days, it seems just getting used to using the hotkey is the most efficient way. It will pop up the documentation for anything at the spot of where your text input marker is so you never have to touch the mouse. This works in the intellisense popup as well and will stay up while navigating up and down.
Personally, Ctrl+Q on windows was not ideal so I remapped it to Alt+D. Remaping can be done under IDE Settings/Keymap. Once in the keymap menu, just search for Quick Documentation.