Breath = Life giving force.
Spirit = The inner part of a person; God's agency.
Although I do not see any scriptural evedence of what you are asking, I can only assume based upon some clues that might support your theories. According to
Genesis 2:7 And the Lord God formed man of the dust of the ground, and breathed into his nostrils the "breath" of life; and man became a living soul. From Strong's concordance we find that the word "breath" is derived from the Hebrew word
neshamaw which means: A puff, i.e. wind, angry or vital breath, divine inspiration, intellect. or an "animal":--- blast, (that) breath (-eth), inspiration, soul, "spirit". The word "spirit" is closely tied in with breath (also found in Strong's concordance) taken from the Hebrew word "ruwach".
Take this information for what it's worth ( a grain of salt), but if God breathed into man, then it wouldn't be difficult to see that animals are given His breath to live as well. Even though I do not find any evedence to support animals going to heaven when they die, it is difficult for me to say that the spirit of the animals will not go on to live forever. JMO.