The NBA superstar hooked his kid up with an early birthday present -- her own private crib in his backyard ... and it's incredible!!!

It's a mini-version of what appears to be LeBron's Brentwood mansion -- a brand new freestanding structure in the backyard complete with a study room, windows, custom flooring and more!

It even has a play kitchen area -- complete with a play oven, stove, fridge and cabinets (don't worry, they're not REAL working appliances).

"Early bday gift my princess!!! Love you baby z," LeBron said.

It's clear Bron is hoping Zhuri will use the home for school work -- he asks her over and over again if she's taking a break from distance learning.

The funniest part of the video is when Bron tracks in dirt on Zhuri's new custom floors -- and she immediately grabs something to clean it up!

Bron can't help himself -- and starts cracking up ... saying, "Oh my bad. I got your floor dirty??!"