Did you formally test for over dispersion first?My models don’t seem to have great fit, and I’d like to be able to consider and account for overdispersion.
A rule of thumb is there is an overdispersion if your residual mean deviance are much larger than 1 [because of the chi-squared proporty that expected value of a chi-squared variable is its degree of freedom].
You have used the most complex model that you can fit to the data to estimate your dispersion parameter. So, your approach to estimate the dispersion parameter to scale the standard error seems correct.
What software you using? It looks like R to me. There is already an option in R to fit a quasi-Poisson model.