1) Is it a gas unit?

2) If this is a simple electric heater, then consider at least doing the demolition yourself (assuming you are somewhat handy). Yes, you will likely be without hot water for 12-24 hours, but you can probably save yourself a lot of money. If the existing heater has working shutoff valves, cut them off, turn off the electrical breaker, and then connect a garden hose to the drain port at the bottom, run it outside, and open the drain. There is a decent chance that nothing will drain out due to sediment buildup, and in that case, you may be stuck paying the plumber to handle the demo, unless you have a strong kid or neighbor who's willing to help. If the tank drains, then you can cut through the supply and discharge lines at the top. Then open the electrical cover, disconnect the wiring, and you can remove the old tank. If you get really ambitious, you could even purchase the new heater and get it set in place for the plumber to connect.

3) Is there seriously carpet in the same space where your water heater is located? Or is the carpet getting wet on the opposite side of the wall from the water heater?