Rather than use eval inside the replacement term you can use a double ee modifier (see the s operator in Regexp Quote Like Operators).

$ perl -le '
> $str =  q{10 09};
> $reg =  q{(\d+) (\d+)};
> $rep =  q{"$2 $1"};
> $str =~ s/$reg/$rep/ee;
> print $str;'
09 10
$
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I hope this is of interest.