Anonymous Monk,
There is no built-in that will tell you if a character is unique in a string but it is easy enough to create one.

my $cnt = $str =~ tr/1//;
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The thing to consider is that it may be better to trade space for time if you have many such tests on a given string.

my %char_cnt;
++$char_cnt{$_} for split //, $str;
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There are a number of other solutions depending on what your situation is.