Would it give a speed improvement to prepare the regex in advance with qr//?

No, it wouldn´t. At least not as long the regex is, like here, the only one within the loop. The qr//-operator is useful when you have the need of matching the same string to multiple regexes/patterns, like in

@p = 
(
    qr/^abc/,
    qr/abc$/,
);

for $f ( @foo )
{
    for $p ( @p )
    {
        do_stuff() if $f =~ $p;
    }
}
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Using qr// doesn´t even help in code like

while ( $foo =~ /^abc/ && $foo =~ /abc$/ )
{
    do_stuff();
}
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because in such a case internal perl optimizations come into play.