I always do this! My parents make fun of me, cuz when I leave I have all this stuff with me, including her baby bag, or as they call it "Mahina's Diaper Bag".
I put in a sweater, some pee pads, a toy, a chew, a few treats, a blankie, her food, and if I'm going somewhere besides a house I'll bring a waterbottle and water dish.
I think it is being responsible, you never know what's going to happen. You don't want to be stuck somewhere without something to give them.

I think it's a great idea.