Source of John Deere line of children bicycle tires?
Very inexpensive rebranded bike with very inexpensive tires which you can't source individually. Nothing wrong with that given that it's a child's bike, but that is the situation. Your chances of finding that exact tire are slim, and there's no really compelling reason for you to hunt it down anyway. 

The product you can get off the shelf is going to be at least as good and likely better. There's no issue with mixing and matching different tread patterns front and rear beyond aesthetics.