There are several packages that can apply the Durbin-Watson test for serial correlation. However, I do not see a package that supports the calculation in the case that once has a GLS weighted regression.
For example, CRAN package lmtest notes in their changelog that they explicitly do not support weighted regressions (yet). Before the recent release, lmtest would not throw an error when passing weighted regressions.
My concern is that the other dwtest packages may also not be explicitly dealing with this scenario.