Dengue is a major threat to public health in Brazil, the world's sixth biggest country by population, with over 1.5 million cases recorded in 2019 alone. Official data on dengue case counts is delivered incrementally and, for many reasons, often subject to delays of weeks. In contrast, data on dengue-related Google searches and Twitter messages is available in full with no delay. Here, we describe a model which uses online data to deliver improved weekly estimates of dengue incidence in Rio de Janeiro. We address a key shortcoming of previous online data disease surveillance models by explicitly accounting for the incremental delivery of case count data, to ensure that our approach can be used in practice. We also draw on data from Google Trends and Twitter in tandem, and demonstrate that this leads to slightly better estimates than a model using only one of these data streams alone. Our results provide evidence that online data can be used to improve both the accuracy and precision of rapid estimates of disease incidence, even where the underlying case count data is subject to long and varied delays.