Laura - dont do it ! Bad girl.
The lens is already slow at 300mm. I dont know that lens of yours but most consumer tele zooms are not sharp at their max aperture, yours being f5.6. So without the 2x TC you may well be having to shoot at f8 to get decent sharp photos. I have to do this on my 150-500 sigma, although my camera lets me shoot at an inbetween aperture of f7.1, but lets call it f8 as thats a full stop from f5.6. When you add a 2x TC, thats 2 stops you add, as already posted above.
This means at 600mm, you are effectively shooting at 2 stops past f8 regarding the light loss, which is f16. If your lens is sharp at 300mm using max aperture of f5.6, then you will be shooting an effective aperture of f11, 2 stops on. Not so good really, and i think the IQ willl be pretty grim
A 1.5x or 1.4x TC would be much better, i agree with the disorderly. You will only lose 1 stop maybe 1 stop + some small change, but please expect a drop in IQ with a TC