Calculate transistor current output
The LED strip is most likely to have current limiting built in to it, so the configuration shown above should work. If you can plug in your LED strip to a 12V supply and measure the current with a meter and it is within spec then switching the LED strip with a low side switch should be fine without additional current limiting. 

If the strip does not have current limiting then you will need to add it.

Let's talk about your switch, it needs work. Q1 will source a lot of current in the the base of Q2. It would be like plugging the base of Q2 directly into the 12V line, if you try this you will probably see smoke. 

Either put a resistor to limit the current in between Q1 and Q2 (but enough to turn Q2 on fully). Do not exceed the TIP31 base current which is 1A.