I purchased a utility trailer to help with my military move is that considered a moving expense

Yes, consider this part of the cost to be able to move your household goods.  

If you should happen to sell that utility trailer in the future it would be considered taxable income (of a previously deducted amount).

Moving expenses can be entered by following the steps here.

1. Select My Account in the upper right 
2. Select Tools 
3. Select Topic Search 
4. Search for  moving > Go (image attached)
5. Follow the prompts to enter your allowable moving expenses (image attached)
6. Click the blue hyper-links for more information as needed.