I was trying to scrap data from the following website

Um, scrap means throw away, recycle, chop into little pieces, melt down

The site does navigate using Javascript. I hear that Java-based can be difficult to scrape using Perl. Should I try some other method?

For the solution to every scraping problem, see Re^5: can't get WWW::Mechanize to sign in on JustAnswer or Web Testing with HTTP::Recorder or WWW::Mechanize::Firefox

 mech-dump http://web1.ncaa.org/stats/StatsSrv/careersearch will show you the noscript version of html, and indeed, one of the fields you try to populate doesn't exist in the html only browser