Gypsy Rose Struggles During Karaoke with Ken Urker, Crushes Songs with Group of Ladies

Gypsy Rose and Ken Urker have a strong connection as a couple ... but, not so much during karaoke -- 'cause they didn't pick the right song for them it seems.

TMZ has obtained video of the happy couple -- who welcomed their first child together late last year -- at Cat's Meow 2 World Famous Karaoke Bar Friday night ... and, they stepped up to duet the track "Shallow" from "A Star Is Born."

Ken's super into the track ... belting out the notes with a passion we bet Bradley Cooper can hear from his place in NYC -- but, when it's time for Gypsy to sing, the confidence just ain't there.

It seems Gypsy misses her cue ... then explains to the audience she doesn't know the song -- a bit shocking given how big a fan Ken seems of it.

However, Rose didn't let the one awkward moment harsh her vibe at all ... 'cause she got up on stage with four other ladies at one point and absolutely CRUSHED two other tracks.

Gypsy and the Roses -- not an official name, but a moniker the group's welcome to if they're trying to go on tour -- sang Taylor Swift's "Blank Space" and TLC's "No Scrubs" ... and, Gypsy nailed every lyric and even moved to the beat with her pals.

It looks like a fun night out for Gypsy and Ken who are busy being new parents ... and, Gypsy's been focused on her fitness regiment, too -- revealing back in April that she lost 25 pounds.