Unless God plans to make us like Vulcans, I tend to believe we will have pets in Heaven and eternity on Earth. It’s our created nature to want to bond.
In light of the passage from Isaiah, I don’t think we are going to actually have pets in heaven as we do here on earth.
It seems like ALL the animals will be in close relation to us. If the child is playing near the animals like that, we will be in great relationship with ALL of them, not just the domestic ones.
JMO.