Hi Sarah Joyce,
As per the description, I understand you are having the personal Microsoft 365 subscription accounts but now due to the business development, you're looking to transition the current account subscription to a business plan that can accommodate you and your two employees, especially to gain access to Microsoft Planner. Please correct me if I made any misunderstanding because I want to make sure I can provide you with the most appropriate suggestions.
Your plan is completely correct as currently Microsoft Planner is not available for Microsoft 365 Personal accounts as it's designed for use with business or educational subscriptions, you may find detailed Business plans info from Compare All Microsoft 365 Plans | Microsoft and choose the one that suits your business management best. Personally, I would recommend Microsoft 365 Business Standard including Office desktop apps. Also, it offers a comprehensive set of features that can help you manage your business more effectively including Microsoft Planner and other business tools.
Then, you, as the tenant admin, create domain and start everything following: Welcome to Microsoft 365 for business - Microsoft Support
After that, if there have important files that are currently saved under your personal account, simply download the OneDrive apps and you can transfer them to your work account following: Move files from OneDrive Personal to OneDrive for work - Microsoft Support
Please correct me if I made any misunderstanding or if there have anything else I can do for you.
Your patience is highly appreciated. Hope you a nice day and stay safe!
Best Regards,
Mia