Purpose. To improve breast cancer risk prediction for young women, we have developed deep learning methods to estimate mammographic density from low dose mammograms taken at approximately 1/10th of the usual dose. We investigate the quality and reliability of the density scores produced on low dose mammograms focussing on how image resolution and levels of training affect the low dose predictions. Methods. Deep learning models are developed and tested, with two feature extraction methods and an end-to-end trained method, on five different resolutions of 15,290 standard dose and simulated low dose mammograms with known labels. The models are further tested on a dataset with 296 matching standard and real low dose images allowing performance on the low dose images to be ascertained. Results. Prediction quality on standard and simulated low dose images compared to labels is similar for all equivalent model training and image resolution versions. Increasing resolution results in improved performance of both feature extraction methods for standard and simulated low dose images, while the trained models show high performance across the resolutions. For the trained models the Spearman rank correlation coefficient between predictions of standard and low dose images at low resolution is 0.951 (0.937 to 0.960) and at the highest resolution 0.956 (0.942 to 0.965). If pairs of model predictions are averaged, similarity increases. Conclusions. Deep learning mammographic density predictions on low dose mammograms are highly correlated with standard dose equivalents for feature extraction and end-to-end approaches across multiple image resolutions. Deep learning models can reliably make high quality mammographic density predictions on low dose mammograms.