Daily adaptive radiotherapy, as performed with the Elekta Unity MR-Linac, requires choosing between different adaptation methods, namely ATP (Adapt to Position) and ATS (Adapt to Shape), where the latter requires daily re-contouring to obtain a dose plan tailored to the daily anatomy. These steps are inherently resource-intensive, and quickly predicting the dose distribution and the dosimetric evaluation criteria while the patient is on the table could facilitate a fast selection of adaptation method and decrease the treatment times. In this work, we aimed to develop a deep-learning-based dose-prediction pipeline for prostate MR-Linac treatments. Two hundred twelve MR-images, structure sets, and dose distributions from 35 prostate patients treated with 6.1Gy for 7 or 6 fractions at our MR-Linac were included, split into train/test partitions of 152/60 images, respectively. A deep-learning segmentation network was trained to segment the CTV (prostate), bladder, and rectum. A second network was trained to predict the dose distribution based on manually delineated structures. At inference, the predicted segmentations acted as input to the dose prediction network, and the predicted dose was compared to the true (optimized in the treatment planning system) dose distribution. Median DSC values from the segmentation network were 0.90/0.94/0.87 for CTV/bladder/rectum. Predicted segmentations as input to the dose prediction resulted in mean differences between predicted and true doses of 0.7%/0.7%/1.7% (relative to the prescription dose) for D98%/D95%/D2% for the CTV. For the bladder, the difference was 0.7%/0.3% for Dmean/D2% and for the rectum 0.1/0.2/0.2 pp (percentage points) for V33Gy/V38Gy/V41Gy. In comparison, true segmentations as input resulted in differences of 1.1%/0.9%/1.6% for CTV, 0.5%/0.4% for bladder, and 0.7/0.4/0.3 pp for the rectum. Only D2% for CTV and Dmean/D2% for bladder were found to be statistically significantly better when using true structures instead of predicted structures as input to the dose prediction. Small differences in the fulfillment of clinical dose-volume constraints are seen between utilizing deep-learning predicted structures as input to a dose prediction network and manual structures. Overall mean differences<2% indicate that the dose-prediction pipeline is useful as a decision support tool where differences are>2%.