Dannielynn Birkhead just took a bite out of the Big Apple.

The daughter of Anna Nicole Smith, who just turned 6 in September, was spotted in NYC with her father Larry Birkhead this week ... where they attended a Broadway show.

So, what'd they see? "Annie."

The two were seen backstage after watching little Lilla Crawford belt out "Tomorrow" and "Hard Knock Life" at The Palace Theater on Sunday night.

Sporting a leopard print jacket, Dannielynn looked like a perfect blend of daddy Larry and her late model mom. It's crazy how big she's gotten ... and how rare it is for Birkhead to take her out in public.

Little Dannielynn made headlines back in November when she modeled for GUESS kids, following in her mother's famous footsteps.

Check out those photos by clicking here.

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