According to Joystiq, a Sony representative informed the site Don't Starve will be available free of charge for PlayStation Plus members when it launches in early January. The PlayStation 4 version will come packed with all of the content that's currently available for the PC version and will be updated concurrently with it in the future.
If you're wondering about the Remote Play features and whether or not you can play it on the Vita, the representative said, "A Vita native version with cross-save is coming a couple months after the PS4 version." And yes, it will support Remote Play so you can start playing on your Vita immediately.
In related news, The Binding of Isaac: Rebirth will also be available for free on PlayStation 4 for PlayStation Plus members when it launches in early 2014. Both titles will see updates on the PC as well once the respective next-gen versions arrive.