One interesting approach to this problem is to think about requirements for Von Neumann probes and if we’ve seen these features in nature.
Thousand year plus high fidelity self replication? Life’s DNA/RNA + cellular mechanism are pretty good at replicating the information and the machinery.
Thousand year plus “continuous” power? Stars - but maybe a ...
This is a great question and it can have several answers depending on propulsion technology. I will address only a solar sail.
171 days! (+30 years of development & approaching the Sun1)
Wikipedia's Heliosphere; heliopause says:
In September 2013, NASA announced that Voyager 1 had crossed the heliopause as of 25 August 2012. This was at a distance of ...