US here, I'm from the Mountain West (Colorado, Rocky Mountains) but now live in the Mountain East (panhandle of Virginia, Appalachian Mountains).

"I forgot my X at P." meaning "I forgot my [item X] and left them at [place P]."

I would call this moderately common phrasing for most items and places and completely understandable. To my ear, at any rate. (However, I don't think that forgetting one's Rottweiler would be common ... anyplace!)

BB,
NightWing