Of course you can bless animals just like you can bless a home or anything else. There is a lot in the power of prayer!
Honestly, I'm in agreement with most who have commented in this thread, with some great quotes and examples. Especially when requested by the owner, though even in general if one feels it may be helpful or am prompted by the Spirit, there shouldn't be any reason why a Priesthood holder couldn't given animals a blessing I feel.
Whether farm animals or pets, we as humans have often shown great attachment and care for the animals under our care. So even if the animals cannot have faith for themselves, we can still have faith enough to have such blessings performed.
I don't see the purpose of this unless it is specifically to heal the animal but healing, when divine, should be instant.
We break from Can Priesthood Blessings Be Given To Animals? to share wise words from yesteryear:
Today is: 11th July (GMT), in history on the 11th of July, 1975 AD the following event happened:
Chinese archeologists discover a 3-acre burial site with 6,000 clay statues of warriors dating as early as 221 BC