How would any bag be an obvious diaper bag? A quick image search for diaper bag shows bags that could just as easily hold laptops or cameras. Parents want to look fashionable too.
The ruse would fail instantly you took the camera out of the bag. Or when you have no child, and look like you are wealthy enough to have a camera hobby.
Not very fashionable, has wet wipes hanging out the side, the pockets have stitched icons for what they're meant to hold like a soother and diapers, etc.
Having a child as a prop would definitely help, but a frazzled look and some wet wipes hanging out the side would probably help it along quite a bit.