Yes. Pets are legally considered property. So, you can include the costs of transporting your pets as another item in your moving expense deduction.
You can read more about the moving expense deduction at the link below -
See the following under Moves to Locations within the United States
"You can deduct the cost of shipping your car and your household pets to your new home"
https://www.irs.gov/publications/p521/ar02.html