Glad to have you here with us in the QuickBooks Community. Let me share to you the list of data you can import into QuickBooks Online.
As of this time, only list of Customers, Vendors, Products/Services, and Chart of Accounts in CSV or Excel file format can be imported into QBO.
You may take a look at available apps that will import transactions from your old accounting software into QuickBooks. I’d also recommend contacting your previous accounting software phone support to assist you in exporting the data and transfer it to QBO.