Hi Alex- There are many types of substitutes for whipping cream that contain no dairy. Some are store bought and others you can easily make at home. In these applications, temperature and the intended use play a large role in how you decide. In this recipe, coconut milk will serve the purpose and add great flavor. In other applications, whipped silken tofu can serve in place of cream.
In cold applications (say, whipped cream for pie) you might use an off-the shelf brand (many contain additives, etc. to stabilize) or you can also whip coconut cream.
Given your interest in plant-based cooking, I might suggest that you try
Rouxbe's Plant-Based Cooking Level 1.
That would be an ideal place to focus your attention to this area if you are interested. Plus, you'll have a community of students to help answer questions like these. Enjoy!