"A Vita native version with cross-save is coming a couple months after the PS4 version," the rep also told us. Either way, the PS4 version will support remote play, so it'll be functional on the Vita when it launches for PS4.
We were also told that The Binding of Isaac: Rebirth, due out in early 2014 on Steam, PS4 and Vita, will also be free to PlayStation Plus members when it launches.
Update: Don't Starve developer Klei informs it's focusing on the PS4 version and remote play functionality at this time. A PS Vita native version is still being explored.
Also, The Binding of Isaac: Rebirth will receive a simultaneous native launch on PS3, PS4 and Vita.