Can you do it?  Yes.  Should you? No. 

Any good propane company should be able to pump it out if the tank has the proper fittings. There is a possibility it can't be done, but very rare for that to happen.

Yes, it will cost a bit.  You have 2 trained employees (probably will take one guy to drive the bobtail and another to move the tank) with specialized equipment handling hazardous material. 

Don't forget that once the tank is moved the system it is connected to will need inspected and brought to code. Pumping out a tank, relocating it, checking out the new system, then filling it again are going to blow a day.

As Marc said, moving it full is illegal.  And whatever you do DO NOT PICK IT UP BY THE EARS.  They are not designed for a 6000 pound load and you risk pulling them out of the tank.  You do not want to be around if that happens.  If it has to be picked up full it needs straps going under it in 2-4 places.

Moving it around the farmstead or resetting a tank foundation is different than moving it 10 miles ... unless you can do it without crossing a road. 

It isn't rocket science but it does take time and the folks doing it need to know what they are doing.