I'd like to enter clients orders in QuickBase and bill the clients using QuickBooks. Is integration done with 3rd parties only?

If you want import a synchronized copy of QuickBooks online data into quick base than that setup is native and quite easy. But if you want to write data from QuickBase into QuickBooks then yes you need a third party integrator. Feel free to contact me off-line if you want some recommendations. I don't do this work myself.