Dependency parsing has received significant attention from the research community due to its recognized applications across diverse areas of natural language processing (NLP). However, the majority of dependency parsing studies to date have not addressed the out-of-domain problem, where the data in the testing phase are in a different distribution compared with data in training domains, despite this being a common problem in practice. Furthermore, Vietnamese is still considered a low-resource language in parsing tasks, as most standard treebanks are primarily developed for more widely spoken languages such as English and Chinese. This shortage pushes the difficulty of studies of Vietnamese dependency parsing task even further. To advance research on domain generalization in Vietnamese dependency parsing task, this paper introduces a new treebank called DGDT (Vietnamese Domain Generalization Dependency Treebank), where domains in train/dev/test set are completely separated. This is the distinction of our treebank, compared to other Vietnamese dependency treebanks. We also release DGDTMark, a cross-domain Vietnamese dependency parsing benchmark suite using our treebank to assess the generalization ability of parsers over domains. Moreover, our suite can support further research in analyzing the impacts of domain gaps on the dependency parsing task. Through experiments, we observe that the performance of parsers is most affected by two gaps: newspaper topics and writing styles. Besides, the performance drops remarkably by 3.27% UAS and 5.09% LAS in the scenario with the largest domain gap, which proves that our treebank poses a significant challenge for further research.