Joe Jonas and "Game of Thrones" star Sophie Turner are so that couple ... y'know the type ... so freakin' happy they're floating on air.

They were skipping through the streets of downtown Manhattan Monday looking like they were having the time of their lives together ... and making everyone around them feel like their lives are crap. 

The couple hooked up last fall, and it's clearly serious since Sophie's wearing Joe's "Overthrow" hoodie.

Sorry, 'GOT' fans ... the gear is NOT a subtle hint for season 7, it's just Joe's boxing gym.