Although the Pi can supply 16mA (ish - drive strength is a poorly controlled parameter) at 5V, energy is conserved. Since Power P = I*V, where I is current and V is voltage, stepping up the voltage means the current supplied to the LED will be lower than the current from the GPIO - even with 100% converter efficiency, you'll get 4.4mA max from a 3.3v GPIO. When we also take into account that
- The converter efficiency will be much less than 100%, especially with such a large step from 3.3V to 12V
- 16mA is the current with the GPIO shorted - at this point, the output voltage is actually zero, not 3.3V. Any significant current draw will cause some amount of voltage drop
We can see that driving a high power LED from a Pi's GPIO is essentially not a good idea.
there is a better way!
A DC-DC boost converter (search ebay) can provide 12V from a 5V supply with a reasonable efficiency (typically ~85%). A dedicated 12V supply is better.
The current through the LED is switched on and off by a transistor - a MOSFET is ideal because no current flows into its gate while it is on.
The MOSFET suggested in the diagram will happily pass an amp or two with a 3.3V gate voltage from the GPIO pin, making the LEDs much brighter and avoiding any damage to the Pi.
This type of transistor circuit (just the lower part) is very useful for driving higher voltage loads from a low voltage microcontroller or processor.