My spouse and I have been in the US for less than a year under residential alien status.

We are both independent contractors.

Do we need to file for a sailing permit? We don't have salary tabs to take to the airport, due to being independent contractors.

Will we need a sailing permit in order to ship our belongings back to our home country?

Also - on return to our home country, we will inform the USCIS of our new address and then receive our tax documents to our home country? Is that correct? Is there anyone else we'd need to inform of our new address in our home country?

Just to clarify - we are planning to permanently leave the US shortly.

To receive your forms from companies you were working for, they will need an address to send the end of the year forms.

Although I haven't heard any case lately that anyone at the airport actually wanted to see the Sailing Permit, you might be required to have one. See here for more information:
Departing Aliens and the Sailing Permit
Some aliens are exempt from filing form 1040C. You can find those rules in Publication 519 (there is a link to that publication on the above mentioned website)