Count Panel Data problems : autoregression and fixed-effect models

Hello Statalist members. I post this message because i have an issue with my analysis.

I have a count panel data set of 719 heathcare facilities from 2011 to 2014.
I need to explain the incidence of bacterias with the consumption of hand-rub solution, then i use an fixed-effect xtpoisson regression : my command is xtpoisson Y X1 X2, fe vce(bootstrap)

Here is my problem :
i have an autocorrelation (i tested it with the woolridge test for autocorrelation in panel data) and i need to use a fixed effect regression (tested by Hausman test).

Do you know if there is a panel count model regression which can asses an AR1 and a fixed-effect ?
Or it is possible to use the xtregar regression or a dynamic model ?

Thanks a lot.

Ugo Desmoulin