Thanks for bringing your question to the Community. To clarify, are you currently using QuickBooks Self-Employed (QBSE) or QuickBooks Online (QBO)? You can verify this by checking the URL of the site you log in to your software at.
The good news is, both versions are cloud-based meaning that they can be accessed in supported browsers from anywhere with an internet connection. Currently, our supported browsers are Google Chrome, Mozilla Firefox, Internet Explorer, Microsoft Edge, and Mac's Safari. Since the Chromebook uses Google Chrome exclusively for web browsing, any Chromebook will be able to connect to QBO or QBSE just fine.
You can learn more about working in QBO from anywhere here. Please be sure to let me know if you're having trouble getting connected so I can lend a hand, I want to ensure your success. Thanks again, wishing you a wonderful rest of your day.