First, I think it important to determine whether or not animals have souls. After all, it is the soul which lives eternally. In the creation of mankind, God "breathed into his nostrils the breath of life; and man became a living soul." (Gen. 2:7). Later, when God decided to destroy all life except those on the Ark, animals were described as also having "the breath of life." (Gen. 6:17; 7:15, 22). It seems logical to me that if God breathing into man made him a living soul, it would also do the same for all those species on the Ark.
The soul is the life force, the very uniqueness of an individual; the personality, if you will. It is who you are. You have a body, and with mankind, you have a spirit. Those born again are said to be alive spiritually; those who are unsaved are said to be dead spiritually. (Jn. 3:3-8; Rom. 6:11-13; Eph. 2:1-5). This is what Jesus referred to when He said, "Let the dead bury their dead." (Mt. 8:22). But I digress.
Animals clearly have emotions, memory, attitudes, etc. Animals have value to God. We read in Luke 12:6, "Are not five sparrows sold for two farthings, and not one of them is forgotten before God?" The Psalmist wrote, "The LORD is good to all: and His tender mercies are over all His works. All Thy works shall praise Thee, O LORD; and Thy saints shall bless Thee. They shall speak of the glory of Thy kingdom, and talk of Thy power; to make known to the sons of men His mighty acts, and the glorious majesty of His kingdom." (Ps. 145:9-12). In other words, creation, including animals, praise God and give testimony to His glory.
And finally, we know there are animals in heaven because the Lord will appear at His Second Coming, riding a white horse, and He will be accompanied by the armies of heaven, all riding on white horses (Rev. 19:11-14). One might also consider these verses (Eccl. 3:21; Ps. 36:6; Prov. 12:10; Isa. 65:25).
The righteous care for their animals;
the wicked treat them cruelly (Prov. 12:10)!