How to use a low current signal to activate my circuit
Here is a classic high-side switch circuit that should work for you.



A couple of points about the transistor choices. You can't just use any P-channel MOSFET for Q1.  Because of the low-ish voltages involved you need a logic-level MOSFET which simply means that the process is tweaked for lower VGS.  Q1 (IRF3708PBF) specifies a max RDSon (resistance) of 0.029 ohms with a gate voltage of -2.8V. Available at Digikey for a couple of bucks. 

So... with a load current of 200mA, Ohms law tells us our IR voltage drop will then be 0.2A * 0.029 ohms = 0.006V of drop. Very little voltage loss - so far so good.

To drive the gate of Q1 low, we use a common NPN transistor at Q2. To avoid turning on Q2 (and Q1) when the CTRL voltage is 0.8, we put a diode in series with the gate. This raises the turn-on threshold of Q2 to about 1.2V.  When Q2 is fully on, you should see about 0.2V at the collector which drives the Gate of Q1 nice and low turning it on fully.

The purpose of R1 is to keep the VGS of Q1 solidly at 0V (OFF) even in the presence of any leakage current at Q2. 

R2 limits current into the base of Q2 when the CTRL input is ON.