Dropping one class her 8th semester will have absolutely no impact on college admissions. They won't even know during the admissions process since they only will see a transcript through 7th semester. You will have to submit a final transcript, but that is only to confirm that they didn't total fail that last semester, and having one less class will not make any impact. Only D's and F's will do that. College admissions is not a valid reason for having a full academic schedule 8th semester.
But, what is your DD going to do with that extra time? Sit a home and play video games and watch reruns of Gilmore Girls. Or is she going to use that time to do something productive? My DD graduated college in 3 1/2 years. She used what would have been her final senior semester to study for the MCATS, continue her research, volunteer at a women's shelter and find a job for her gap year. Although she had no classes it was a very productive time for her. What is you DD going to do instead of taking psychology?