"For the record none of us hunt, just enjoy shooting for sport. I'm raising the kids with knowledge of fire arms, how to handle them, shoot them, store them, and avoid them in uneducated hands. #knowledgeispower," he wrote.
In the clip, Willow is seen wearing protective noise cancelling headphones.
"Can I go?" she asks her dad who replies, 'whenever you're ready'.
Being extra cautious Willow then adds, 'Wait, is the safety on?' before Carey confirms she's good to go.
Social media users were broadly supportive of Hart teaching his daughter about gun safety but some questioned the move.
"In this day and age it is time for new thinking instead of following tradition and culture. The fact of the matter is that guns are killing people — children for that matter — don't you have to agree that we need some kind of reform?" @Ashleighbiasi wrote.
@cherylinoh wrote "Unless she loses control and shoots you in the face."
Pink and Hart also have a son, Jameson, who turned two last month.