Hm, that seems a little extreme given that NASA is still communicating with Voyager at a distance of 10 billion miles and Voyager's dish antenna is only 2.7 meters wide. Also, I've just found a web page stating that "Both Voyagers are so far away from Earth that only the largest DSN antennas — 230 feet in diameter — can send commands to the spacecraft. To do that, they use a 20 kilowatt S-Band transmitter. That's about one-half to one-quarter of the power transmitted by an ordinary commercial AM or FM radio station on Earth."
So I still hold out hope that a nuclear generator is unnecessary, though I am starting to think my heroine may need to remotely hijack one or more of the antennas used by NASA's Deep Space Network to get the job done...
AG was somewhat over the top
You already know what is required, high power (particularly for the frequency in use) and a MASSIVE dish - fairly obviously, you could use lower power and a MUCH smaller dish, as long as the other end has a massive dish and high power, and is perfectly aligned at the required time. Perhaps your story could reflect this? - you mention 'hijack' existing equipment, this is probably the most plausible scenario, but has been done numerous times in SciFi stories.