This might be a question for testing advanced speakers of English to see if they can catch very small differences in meaning. Both answers are perfectly correct, natural, and idiomatic. Both words mean that the speaker admires the plan, but they are not exact synonyms. As a matter of style and word choice, "ingenious" might be better. "Brilliant" is just a way of saying the plan is very good. "Ingenious" means that the plan is full of clever, surprising, original inventive details. Therefore--in my personal opinion--"ingenious" is a better fit with "a lot of imagination" than "brilliant." "Ingenious" does not necessarily mean "good." Look up the funny cartoons of Rube Goldberg or Heath Robinson for examples of crazy inventions that are ingenious, but would never work." It is possible to say "It took a lot of imagination to come up with such an ingenious plan--but it's no good." Imagine two people have parked in a giant airport garage. "We have to remember our parking space." "We are on level H, zone 9 so I'll just remember that my aunt's name, Henrietta, starts with an H and has 9 letters." "That's very ingenious! But it's so complicated. I'm just going to take a picture of the sign with my cell phone." "That's simple, but brilliant!"

I would say either is correct, so long as you say "a brilliant plan" and "an ingenious plan" (correct article use). Ingenious might be more emphatic, but that can depend on intonation too.