Do dogs go to heaven?

20 For the creature was made subject to vanity, not willingly, but by reason of him who hath subjected the same in hope,

21 Because the creature itself also shall be delivered from the bondage of corruption into the glorious liberty of the children of God.

in other words:
The creature (animals) shall be delivered from corruption that sin has brought up them and shall enjoy the same glorious freedom from this evil world that the children of God shall experience.

Is being 'delivered from corruption' a resurrection and transportation to heaven or a final death and new creation?

No the creature is not resurrected. No creature will be up in heaven . There will be on the new earth but not the dead once the new creatures.

ok...so the creature being 'delivered from corruption' and receiving 'the glorious liberty of the children of God' is it's final destruction when Jesus comes? Jesus will kill all the animals and that's called deliverance and liberty for them? If they share the same liberty as the children of God, then are the children of God destroyed too?

I think God is talking generally. Meaning the animals would get liberty taken away but not the same way as man. They get to come back as a species.

Rev.19:11 And I saw heaven opened, and behold a white horse; and he that sat upon him [was] called Faithful and True, and in righteousness he doth judge and make war.
Could be symbolic.
 The animals alive on the earth, when Jesus comes will not be made to suffer, mankind has been very cruel to the animals. We have a merciful heavenly father

This might be symbolic.