Yes, you certainly can import customers, suppliers and employees. Customers and suppliers can be imported from Outlook, Gmail or as an Excel spreadsheet and you can find detailed instructions here. This page also answers common questions on importing data to QuickBooks Online.
Importing employees can be done using an Excel spreadsheet - see here for detailed steps on this process. You can also import your Chart of Accounts, products and services, invoices, bills, and historical bank data.
As addtional option, you may utilize the trial period of TP as migration tool.
If you have to open a new QBO account, make sure to click the Buy button to get the discounted price for up to a few months. If you purchase from the trial account or upgrade/downgrade plan, you have to pay the regular price.