Altima 2006 2.5 S Code P0462 = Fuel Level Sensor A Circuit, Low Input Fuel Gauge Is Inop

Fault Code P0462 reads out - Fuel Level Sensor Circuit Low Input and could be caused by -

- Faulty fuel level sensor
- Fuel level sensor harness is open or shorted
- Fuel level sensor circuit poor electrical connection  
- Combination meter

Since you're getting the right output when the tank is topped up, this is most likely a failing sensor.
The check light is set-off when -

An excessively low voltage is sent from the sensor is sent to Engine Control Module (ECM)

Possible Symptoms -

• Engine Light ON (or Service Engine Soon Warning Light)
• Incorrect fuel level reading

You're getting both.
Info specific to the Altima - 2006

The fuel level sensor is mounted in the fuel level sensor unit. The sensor detects a fuel level in the fuel tank and transmits a signal to the Engine Control Module (ECM). The fuel level sensor consists of two parts, one is mechanical float and the other side is variable resistor. The fuel level sensor output voltage changes depending on the movement of the fuel mechanical float.

You could try resetting the code, checking all the connections, topping the fuel up again and seeing if the problem persists.
If it does, you'l need to replace the fuel level sensor as you rightly surmised.
I'm not sure where and whether you'l be able to buy this part separately, but it surely doesn't warrant a fuel pump replacement.
Source engine-codes.com
Good-luck