Do I have time?
This can be found on the school’s website.
First, Princeton has SCEA not ED.
Second, it is recommended that test scores should arrive by 11/1
If anything is still unclear you should contact admissions and ask for clarification.
https://admission.princeton.edu/applyingforadmission/single-choice-early-action
My son took the SAT subject tests in October and the scores arrived early November (2011). At the time we called admissions and ask if we should pay the extra amount to have the test scores rushed to them. They said no and that basically it was a waste of money. When my son received his scores, he self reported them to Princeton. The official scores arrived at Princeton’s admissions office sometime around the second week of November (these are simply used to confirm your self report). He received an offer of admission in mid December (recruited athlete).