Getting ready for a 6-7k mile trip, the tires on the truck have 36k on them. They measure 8/32nds vs 15/32nds when new (the spare). The old standby method is using a penny to show worn out tires ...
I don't like starting out on a trip with components that are near end of life. Maybe I am just overly conservative, but for my own peace of mind, if I were in your shoes, I would put new tires on it before leaving town.