DHT11 Sensor : Stand-by or Shut down?
At times like this it is useful to refer to the datasheet.  You can, in that document, find this paragraph:


  4. Power and Pin
  
  DHT11’s power supply is 3-5.5V DC. When power is supplied to the sensor, do not send any instruction to the sensor in within one second in order to pass the unstable status. One capacitor valued 100nF can be added between VDD and GND for power filtering. 


So you can see that if you power down the sensor completely you have to wait at least 1 second before you can do anything with it.

With it just in the low power mode it defaults to between readings you can immediately start reading as soon as your ATMega wakes up.

So you have to ask yourself: Does running the ATMega at full power for 1 second consume more or less power than running the DHT11 in low power mode for 8 seconds?

As a rough guestimate - if the ATMega is using 30mA (ballpark figure) for 1 second (that's 30mAs - milliamp-seconds), and the DHT11 uses 50uA for 8 seconds, then you have 0.05*8 = 0.4mAs.  

That's 0.4mAs (sleeping) vs 30mAs (powered down). So I'd go for leaving it powered and avoid the one second delay at full power.

Another option that may save more power would be to:


Power off the DHT11
Sleep 8 seconds
Power on the DHT11
Sleep 1 second
Read DHT11
Go to 1


Of course, that means your loop then takes 9 seconds not 8. You could compensate by sleeping for multiple amounts to make 7 seconds:


Sleep 4 seconds
Sleep 2 seconds
Sleep 1 second
Power on the DHT11
Sleep 1 second
Read DHT11
Power off the DHT11
Go to 1


But of course that then makes your sleeping less efficient - so is it really worth it?