Quasipoisson or negative binomial glmm with differing dispersion by group

Question

I have a set of count data, which look something like this:

    Count   Count.type   Site
    299     A            A   
    325     A            A       
    192     A            A       
    180     B            A       
    304     B            A       
    332     B            A       
    2919    A            B       
    2014    A            B       
    2220    A            B       
    1967    B            B       
    1799    B            B       
    2001    B            B       

... and so on. There are only two levels of Count.type, and about ten Sites.

I'd like to fit a model similar to:

glmmPQL(Count ~ Count.type, random = ~ 1 | Site, family="poisson")

My problem is that the dispersion of counts is dramatically higher for one level of Count.type than for the other. I have tried to find a negative binomial or quasipoisson approach, but in the examples I can find (e.g., here How does glm.nb work?), a single theta is estimated and used on all groups.

Does anyone know of a solution that would estimate (or allow me to manually specify) different dispersion parameters for the two groups in Count.type, that is robust for count data?