My main goal is to model some count data. The dataset is a time series dataset that if I were to perform linear regression, I would difference to make sure the data became stationary. However, if I want to use Poisson GLM, would I still difference it or try to make stationary? My main concern is if I were to apply a transformation, I wouldn't be modeling counts anymore, rendering Poisson irrelevant. In addition, differencing can lead to negative values, and Poisson is only for positive values.
If you need to model longitudinal data where the outcome is a count, I'd recommend using a mixed model approach or a Generalized Estimating Equations (GEE) approach. Both of these methods will account for the serial correlation of your outcomes and you will not have to worry about transformations or taking differences of measurements. A search on this site for GEE/Poisson or Mixed Models/Poisson will lead you in the right direction.