No, just go to Image>Resize>Canvas Size. Make it as big as you want - in fact, make it bigger than you want.
At the bottom, make sure the "Canvas Extension Color" is white. I know it's tempting to make it black, but it's risky. Leave it white.
Once you've done that, and hit OK, add a black Solid Color layer, then invert the mask, then paint the black onto those outside areas. Use a nice biggish soft brush, so the new black blends with the existing black.
Lastly, turn that layer on and off a few times, to make darn sure none of your new black has encroached onto the baby.