First of all, I'd like to apologize for my initial answer as I completely missed your key issue about utilizing Power BI Online. Allow me to try to make amends by attempting a more complete and proper answer.
In the case of Power BI Online, because the Power BI-to-DocumentDB connector is currently in beta, it is not available as a data source within Power BI Online under the Get Data section as you noted. Saying this, you can create a connection to DocumentDB using the Power BI desktop, publish it to Power BI Online, and then refresh it within Power BI Online. Following the "Power BI tutorial for DocumentDB: Visualize data using the Power BI connector" tutorial, here is a screenshot of running the data refresh on PowerBI.com using the credentials to your DocumentDB database.
Note, there are is already a request on the Power BI Ideas forum to have DocumentDB available directly within Power BI Online - you can read more and vote for it (if appropriate) at: https://ideas.powerbi.com/forums/265200-power-bi-ideas/suggestions/7160908-documentdb.
Some additional references that may be helpful:
- Data Refresh in Power BI: Here is some additional information about how Data Refresh works in Power BI.
- Power BI Content Packs: For more information on connectors between Power BI and other data sources, please reference Content Packs.