The commute to your new job has to be 50 miles further than the commute to your previous job (from your old house). This means that if you drove 20 miles to your previous job the commute to your new job needs to be at least 70 miles. Also you have to work full time for at least 39 weeks the first year after you move. This is to ensure you moved for a job. Under these circumstances all of your moving expenses (including car transport) are tax deductible.
If you prefer to drive your car to your new home you can still get some tax breaks. Gas and lodging during the trip are deductible, but wear and tear on the car, depreciation in car value, or added insurance costs cannot be deducted.
Your employer may cover the cost as well. It’s smart to ask about this as coverage may not necessarily be provided otherwise.
Work with your broker to make auto transport work for you.