MOSFET and LED Circuit
Your concept is not completely wrong, but there are some things to keep in mind:


9V may not be sufficient to supply 6 LEDs in series, since the total voltage drop will be the sum of the individual forward voltages. Consider connecting two series of 3 LEDs in parralel instead.
An LED's significant operating parameter is its current, not the voltage applied. As the voltage across an LED decreases with rising temperature, the LED current will increase due to self heating, which leads to a thermal runaway and possible damage to the LED. Use a series resistor (or a constant current source) to limit the LED current to a reasonable level.
In the datasheet you linked in your question, RDS(On) is only specified at VGS = 10V. At VGS = 5.5V, RDS will most likely be low enough for your application. However, at VGS = 1.5V, RDS will not allow any significant current flow through the LEDs, resulting in a faint glow at best. A logic level mosfet like the IRLI520 requires a lower VGS value to reach its minimal RDS.