Because content-type' => 'application/json' you have to json encode the content

#!/usr/bin/perl
use strict;
use warnings;
use HTTP::Request::Common qw( POST );
use LWP::UserAgent;
use Encode qw(encode_utf8);
use JSON::MaybeXS qw(encode_json);

my $ua = LWP::UserAgent->new;
my $data = {
    '401k_contributions'     => 0,
     business_income         => 0,
     charity_contributions   => 0,
     child_dep               => 2,
     filing_status           => 2,
     interest_paid           => 0,
     medical_expenses        => 0,
     nonchild_dep            => 0,
     ordinary_income1        => 150000,
     ordinary_income2        => 0,
     other_itemized          => 0,
     qualified_income        => 0,
     sl_income_tax           => 0,
     sl_property_tax         => 0,
     ss_income               => 0,
};

my $content = encode_utf8(encode_json($data));
    
my $req = POST 'https://tax-calculator-api.taxfoundation.org/taxcalc/t
+cja_submit',
        Host              => 'tax-calculator-api.taxfoundation.org',
        Connection        => 'keep-alive',
        Origin            => 'https://taxfoundation.org',
        'User-Agent'      => 'Mozilla/5.0 (Windows NT 10.0; Win64; x64
+) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/69.0.3497.100 Safari/
+537.36',
        'content-type'    => 'application/json',
        Accept            => '*/*',
        Referer           => 'https://taxfoundation.org/2018-tax-refor
+m-calculator/',
        'Accept-Encoding' => 'gzip, deflate, br',
        'Accept-Language' => 'en-US,en;q=0.9',
        Content           => $content ;
    
#print $req->as_string;
print $ua->request($req)->as_string;
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