During a couple of periods in my life I had a pet dog, each time I was caring a lot for my pet. It hurt so much to lose the pet I cared for. But I know that God, who is love, cares for the creatures of God's creation far more than I or others would. As prophecies show, animals will live unharmed and never harming any in the eternity of the new restored creation, which creation now groans for, with the redeemed of humanity, the repentant believers. As asking for God's will on earth as it is in heaven should be sincere, God's will as it is in heaven should start in our lives. So now I do not live in a way that will mean harm to any of the creatures, which God cares for. It is not just pets that we might care for. All creation now groans for that hope, when the saints of God will be revealed. I would not still contribute to the suffering of any of them.
I would still gladly care for a pet, though I would dislike losing one again, it would still hurt when I care that much. I will need still a place that would be a happy home for any animal I care for, for the rest of their life, so I have to be more ready for that first.