Detecting COVID-19 patients using Computed Tomography (CT) images of the lungs is an active area of research. Datasets of CT images from COVID-19 patients are becoming available. Deep learning (DL) solutions and in particular Convolutional Neural Networks (CNN) have achieved impressive results for the classification of COVID-19 CT images, but only when the training and testing take place within the same dataset. Work on the cross-dataset problem is still limited and the achieved results are low. Our work tackles the cross-dataset problem through a Domain Adaptation (DA) technique with deep learning. Our proposed solution, COVID19-DANet, is based on pre-trained CNN backbone for feature extraction. For this task, we select the pre-trained Efficientnet-B3 CNN because it has achieved impressive classification accuracy in previous work. The backbone CNN is followed by a prototypical layer which is a concept borrowed from prototypical networks in few-shot learning (FSL). It computes a cosine distance between given samples and the class prototypes and then converts them to class probabilities using the Softmax function. To train the COVID19-DANet model, we propose a combined loss function that is composed of the standard cross-entropy loss for class discrimination and another entropy loss computed over the unlabelled target set only. This so-called unlabelled target entropy loss is minimized and maximized in an alternative fashion, to reach the two objectives of class discrimination and domain invariance. COVID19-DANet is tested under four cross-dataset scenarios using the SARS-CoV-2-CT and COVID19-CT datasets and has achieved encouraging results compared to recent work in the literature.