Are there companies that will move one piece of furniture for you? There are, and they're called package and movers. Depending on your needs, these companies can either pack and move all of your belongings for you, or they can simply move one specific item for you. 
Any company that offers this service must first meet certain qualifications and regulations set by the government. This is to ensure the safety of both the customer and the movers themselves. 
When choosing a package or moving company, be sure to ask about their rates and services. Also, make sure to get a estimate of how long it will take them to complete the task. 
Once you've decided on a company, give them a call and schedule an appointment to have them come and take a look at your belongings.