Ladies and gentlemen, I give you your totally-not-in-an-insular cult members.
A thousand years is a long time, and the world will be so different that it's hard to make any concrete predictions. But yes, if I had to wager, I'd bet that what humans conceive of as "labor" in 3026 will still be whatever difficult or annoying bits are done by humans.
In 1026 nearly all labor was agricultural labor. If you told a Roman peasant that magical self-driving contraptions could sow and reap the fields, he might wonder what could possibly be left for humans to do in such a world. And yet, here we are, and I still have to update JIRA tickets.
For my myself, I expect AI to prove a more transformative technology than Docker but less transformative than the sewing machine.