[dredmorbius]

The Voyager probes transmit with a signal of about 23 watts, and are detectable (against a near-silent background) at a distance of about 0.002 light years (20 billion km):

<https://public.nrao.edu/ask/how-strong-is-the-signal-from-th...>

Signal attentuation follows the inverse-square law. A 1 kW signal is 43 times stronger than the Voyager's transmitter. It should reach about 6.6 times further.

So your 1 kW transmitter, if coming from a quiet noise floor (which the terrestrial environment is not) could reach at least 0.01 light years. Possibly further.