Brooke Hogan's Friend was Dog Sitting When Her Pomeranian Went Missing

Brooke Hogan's missing dog, Molly, is out wandering the streets looking for her owner ... at least that's why Brooke thinks she bolted 24 hours ago.

Brooke tells us she left her 11-year-old Pomeranian in the care of a friend for the first time while she went out of town, and left some very specific instructions that weren't followed.

Brooke says she got the bad news while she was mid-flight and hurried home. She's back in Van Nuys, CA now ... searching for Molly. So far, no dice.

We're told Molly was last seen by a neighbor around 3 PM Monday, a few blocks from the dog sitter's home. As for a tracking chip ... Brooke explained why Molly doesn't have one.

Brooke's offering a "very nice reward" to anyone who helps get Molly home safely.