The application of state-dependent speciation and extinction (SSE) models to phylogenetic trees has shown an important role for traits in diversification. However, this role remains comparatively unexplored on islands, which can include multiple independent clades resulting from different colonization events. To explore whether assuming no dependence on traits leads to bias in inference on island dynamics, we extend an island biodiversity model, DAISIE (Dynamic Assembly of Islands through Speciation, Immigration and Extinction) to include trait-dependent diversification simulations, and evaluate the robustness of the inference model which ignores this trait-dependence. Our results indicate that when the differences between colonization, extinction and speciation rates between trait states are moderate, the model shows negligible error for a variety of island diversity metrics, suggesting that island diversity dynamics can be accurately estimated without the need to explicitly model trait dependence. We conclude that for many biologically realistic scenarios with trait-dependent diversification and colonization, this simple trait-less inference model is informative and robust to trait effects on colonization, speciation and extinction. Nonetheless, our new simulation model may provide a useful tool for studying patterns of trait variation.