How would you calculate the Price Elasticity of Demand if the Prices are constant, given that there is change in quantity demanded?
it does not make sense to use the formula for the elasticity like this.The PED is used for theoretical purposes in static equilibrium analisys. If you want to measure the elasticity empirically, then you must use the correct econometric technique, given your dataset.

One simple way is to run a linear regression (OLS) after a log-transform in your data. The parameter estimated captures de per cent sensibility of you endougeneos variable (demand) to your explicative varible (price). 

Don´t forget to check if the parameter statistical significance, you may need more data.