Cleveland Cavs star Derrick Rose just got a brand new family member -- he's adorable, he's furry and he ain't cheap! 

TMZ Sports has learned Derrick and GF, Alaina Anderson, brought home a 10-week-old Chocolate Goldendoodle puppy this week from Murphy's Doodles, a high-end breeder in Florida.

We're told ... the couple dropped $4,600 for the pooch -- which they immediately brought out to their home in Beverly Hills. 

So far, we're told the dog doesn't have a name -- but they're workin' on it!