That's a very cute picture. I had one of those fearless kids, unfortunately, his mom got him too scared. So he now prefers video games to reality. We're working on him, though.
I did get him a little scared too, at least enough to keep him from running out into the street.
I hope you can strike a better balance with your favorite little girl there, but they don't come with good instruction manuals.
Now I'm sure that cute little fruitless mulberry will grow into a monster, killing everything underneath it, with knobby roots coming up to the surface and attacking your slab/foundation. Assuming you can keep it watered.
I'd suggest planting a slower growing Plan B tree to take over before that time comes. Maybe a Joshua tree.
And/or you could follow an old Texas tradition and put in the PPPDS - Prickly Pear Perimeter Defense System. A row up by the fence would give a nice surprise to anyone who decides to drop in the back way.
Generally this system provides a loud audible warning as well as considerable discouragement to the intruder.
To be fully traditional, you eat prickly pears - burn off the spines first - and then arrange for their seeds to be deposited back by the fence wrapped in fertilizer, if you know what I mean.