Absolutely normal! AND when you experience this when pumping, it doesn't even mean that you actually have less milk in one breast, but just that is doesn't pump/let down as well as the other. I experienced the same thing and know this from many other moms as well.
Even the best pumps are less efficient at emptying your breasts than your baby, so even after pumping she will probably get some milk.
Since breastmilk changes over the duration of the nursing/pumping session (foremilk/hindmilk) I would not advocate pumping prior to every feeding.
BUT if she doesn't usually empty both sides when nursing, you can nurse one side, pump the other and then let her finish the pumped side.
Good luck!