Really „Gone on to the Dog“?

Sometimes the strangest things go through my head. Not that I have any reason to be dissatisfied, as there's little to complain about my human family and our stylish home. But, you know, sometimes one just has these thoughts.
Oh, I haven’t introduced myself yet. I’m Suki, a Black Tri Australian Shepherd lady – the house and hotel dog here at the LEDERER’s. Many of you know me and are aware of my charm as a diva on four paws. So, I’m lying there quite relaxed in front of the reception, pondering and gazing at the elephant, whose body and organs are wildly draped on the floor before me. You’re probably wondering how a 24-kilo dog like me could have taken down an elephant, especially in Austria, where we definitely don’t have any roaming around.
Relax. Sabine, my dog mom, is a real gem and never forgets me when she's out shopping. Today, she brought me another “Pet Toy,” which the manufacturer claims is extremely durable (wink, wink). It took me less than 10 minutes to take it apart – almost a new record. Now that’s what I call anger management.
But back to my thoughts from the beginning of the story. A few minutes ago, Matthias, a regular hotel guest, came to the reception and told Sabine that he has now also "gone on to the dog." And since then, I can’t get it out of my head. What does "gone on to the dog" actually mean?
Did Matthias, in a fit of excessive enthusiasm, discover riding dogs and managed with difficulty to mount his 6-month-old Goldendoodle, or what? I have a vivid imagination.
Maybe there’s a mountain I don’t know about yet, named “Dog,” that Matthias climbed yesterday afternoon. Or perhaps he meant the “Hundstoa, meaning dogstone” which actually exists nearby.
Never mind. Matthias continues talking with Mom, and suddenly it dawns on me what they mean. Goldendoodle is Matthias’s first dog, and so when the dog moves in, the person “comes on to the dog.”
Relieved, I trot over to the soft carpet in front of the glass cabinet and curl up there quite self-satisfied. What a clever dog I am. And I know exactly that humans are twisting things here again. Because let’s be honest: we all know it’s completely different when it comes to who came to whom. There’s no doubt about that.

Cheers and see you next time,
Your Suki

Postscript from Sabine:
Because I was curious, I asked Wikipedia. Actually, "gone on to the dog" is an idiom meaning “to fall into dire (financial or health) circumstances.” However, the phrase is also jokingly used in a positive sense by dog lovers.