Going with just facts, I agree that since we are made in God's image that the whole Bible points to a relationship with God through Christ Jesus. Mankind is the only living being on this planet that will be classed as children of God so long as we're born again and the Bible focuses on this fact because it is so important.
However, the only way I can get my head around the concept of creation (including our pets) and the new heaven and new earth spoken of in Rev 21:1-5 has been to liken it to a complete 'system overhaul'. This current world that we live in is broken and imperfect and will be made new. When made new the content/creatures of creation will be there.
The Bible makes reference to the old heaven and earth being destroyed (2 Peter 3:10, Rev 21:1, Matt 24:29) and the Lord will bring down a new heaven and new earth where creation will co-exist without harming each other (Is 65:25). I explained to my older child that it was like wiping Windows 10 off an old computer we had and replacing it with a better operating system - the buttons to open apps etc were still there facilitate us only they were better.
If there is a so-called complete 'system reboot' where lions, wolves, lambs and the rest of creation are present and can live, where current predators will not hunt current prey, one has to wonder about our pets. As people have said earlier so long as we magnify God by enjoying what He has made and being good stewards of it (treating and caring for our pets), if Abba sees how we have been on this broken earth who is to say what decision the Lord will make when it comes to our pets in the new heaven and earth? One thing I'm certain of my cats could sense things during prayer moments which matches up with Romans 8:19-21 and there was an occasion when one of the cats veered away from one of my daughter's friends who turned out to have dabbled in witchcraft.
From what I've read it's a win-win either way. I will either not remember the former things as per Isaiah 65:17 or with our resurrected bodies (1 John 3:2) we shall be like Him and speak into existence a house full of our loving pets in Jesus' Name (Mark 11:14 and 21-24).
Finally seeing my cat die last Friday enabled me to understand this a little better - he just ceased to breathe anymore. It did not negate the heart ache of seeing him go, nor the tears. But now I reflect, there were things I witnessed when my dad gave up his spirit which I won't share here but it was definitely different and two separate things to witness.
Both were still painful but yet two very different occurrences took place when they happened.
Anyway I've rambled - I guess I sit somewhere in the middle of what everyone has said
. It will be one of those things I look forward to asking the Lord when Jesus takes us.