Law enforcement sources tell TMZ ... Brooke has maintained custody of the dog -- for now -- because LAPD's Animal Cruelty Task Force determined the pooch is not in immediate danger.

As we first reported ... the Animal Cruelty Task Force launched an investigation after Brooke mistakenly uploaded video showing her shoving and berating her Doberman named Sphinx.

Our sources say the video itself does not show enough proof Sphinx is in immediate danger under Brooke's care, and that's why the dog has not yet been removed from the home. Of course, that could all change.

We're told LAPD could take the pup from Brooke once the investigation wraps ... if investigators determine she abused the pet.

Brooke issued a long-winded apology after the video surfaced and she caught tons of flak online ... saying it's too expensive to hire a trainer and claiming she's NOT a dog abuser.