Jason always protected kids, so when Bruce and his new spouse had you, it was no exception, since Dick lived in Bludhaven now Jason usually babysit as he 'volunteers' aka, grabbing you and walking off, your only one years old so he's careful around you obviously.

One morning, he overheard Bruce talking to Alfred about if he'll watch you as Alfred handled chores today, and Bruce was at his business meeting. So Jason just walked in to pick you up from the floor.

"I got it, don't worry."

Jason held you as he didn't give the older men an option. He was going to take care of you regardlesd.