Migrating from QuickBooks to any other program is likely to be a involved, Intuit does not really want you to move away so they do not provide the tools that readily allow it. QuickBooks is also primarily a business accounting program so it is not really comparable to Moneydance.
QuickBooks does not allow exporting to QIF, which is the main format that is used to migrate between software programs. Only the Intuit Interchange Format (IIF) is supported.
An IIF to QIF converter will not solve the problem either, as journal entries cannot be exported in IIF format, only lists are exportable.
A somewhat viable way to overcome this problem may be to set up a journal report, to show all journal entries. Print the report using the "print to file" option. Set the file type to Excel before printing. Rename the extension of the resulting file from PRN to CSV.
The CVS importer in Moneydance may be able to handle this file but this is unknown as I have not seen any files produced by QuickBooks and have not found any references about the files produced
You may be able to use the XL2QIF Excel macro that is available to convert the CSV files to QIF. The CSV file may need to be reorganized to generate the appropriate format for the macro to work, such as separating check accounts from term deposits, etc. The above referenced Excel macro supports split transactions.