Even if you do plenty of dead-lifts at the gym, a piano is too big of a load to tackle on your own. But regular movers might not be the best option - there are local piano movers near you that specialize in transporting these delicate instruments so the tune and quality of sound are not impacted by the jolt of a move.
Even if a company is properly insured, you don't want anyone getting hurt on the job, and you'll need to make sure that your prospective company has the right tools to make the job easy and pain-free. While the special dollies that piano movers use don't come cheap, if a company doesn't have these tools, you can't trust them to do the job right.
But piano movers shouldn't charge more than $1,000 no matter where you want your piano put. Base rates usually start at around $200, and you should compare the rates charged by a few different companies near your location before you make a final choice.
Check out reviews online to learn what other customers think of each company you're considering.