Which requires defining sin and culpability, and the consequence of it. An interesting theological question to be reasoned out. To sin does not require "eating the apple" (though Gn. 3 does not say what kind of fruit it was), as angels sinned before that. But the point is that animals do not have inherited sin (not that i see infants culpable of this), which at length leads to the certitude of actual sin in the morally culpable.
But as being under the curse, the wolf and the lamb do not feed together well, and while "sin is the transgression of the law," (1Jn. 3:4) that applies toward those who are under the law.
Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be stopped, and all the world may become guilty before God. (Romans 3:19)
While the Law was given to men, yet dogs are under the law of their master who indirectly enforces aspects of that law and which dogs can break. But they would not be culpable of actual sin unless they could choose otherwise. Yet i think dogs (whom i have found memories of) can seem to express guilt over doing what they know was wrong, and may face punishment by them.
So in principle we may say a dog can do wrong, but not having a God consciousness (worship is an activity peculiar to man), even repressed as with many man, then they were never guilty of disobedience to Him and facing judgment accordingly. Nor are they treated as having eternal spirits, or mentioned in teaching on the resurrection and being rewarded.
Thus while dogs may be culpable to their masters for choosing to do wrong, they face no eternal punishment, and while animals do not now evidence a God consciousness, and are not mentioned as spirits going to Heaven as with man upon death, or being in the bodily resurrection, yet all creation will one day praise the Lord, and with God all things are possible, if not being contrary to His word.
And every creature which is in heaven, and on the earth, and under the earth, and such as are in the sea, and all that are in them, heard I saying, Blessing, and honour, and glory, and power, be unto him that sitteth upon the throne, and unto the Lamb for ever and ever. (Revelation 5:13)
To speak a language with the mouth requires certain physical capabilities, most of which are not found in the other animals on the planet. Thus it is likely that the praise will be ascending from the mind of the creature. I have concluded that Balaam's donkey spoken in Balaam's mind, and that God 'touched' Balaam's mind to hear and comprehend the thoughts of his donkey. It is a sure thing that the donkey was 'seeing' more than Balaam was seeing, until the Angel revealed to Balaam. I have extended this notion to the Garden scene and Eve 'hearing' in her mind the thoughts of the serpent. Could it be that animals, and in particular our beloved animal companions 'hear' in their mind the thoughts of love we have toward them? Our lack of being able to do this 'hearing' may well be a protection for us, so that we remain in a faith-needing regimen until The Lord Translates us to our new bodies/souls.