Parking lot dilemma

So I went grocery shopping alone with my infant the other day. But when I went to put the groceries in the car, I was stumped.
Do I:
1) Put baby in the car first, then load groceries and leave baby in car to return cart? or
2) Load groceries first, then return cart with baby still in it, and carry baby back to car with me?

It was cold out, so I put baby in the car first, but while returning the cart to the corral, I realized the car was unlocked and somebody theoretically could have opened the car door and took the baby.

Or am I just a paranoid new mom?