Is there a way to send a trade to a specific person containing a pet or an inventory item? 

Thanks

Yes, via private sales, either on the pet's page or from the inventory itself.

Inside inventory, click on the item. Select sell. Put in the person's name and the price and a message if need be.

The private sale for a pet is basically the same. Just click the button on the right side of the pet's page, put in the recipient's name and the price, and click ok.