Is there R functions that allow to test for overdispersion when fitting a model with survey design?

I realized I need to use the package survey to be able to include sample weights in my regression analysis. Initially, I wanted to use a negative binomial regression on each one of my outcomes as count data is more often than not overdispersed, so I tried using svyglm.nb. However, for one of the outcomes which has small values, svyglm.nb makes my program crash, so I think there might be some convergence issue. I thought using a Poisson regression might solve the problem, but I would like to be able to test for overdispersion before doing this. There are plenty of functions that test for overdispersion for glm objects, but I was wondering if there were any way to test this hypothesis when the object is of class svyglm and to determine if it is okay to indeed use a Poisson regression?