Problems:

• The first thing that happens is that the end of the operator is found. The only characters to which the parser pays attention at this stage are «\» and the delimiter(s). This means the first «\» in your selector is taken as the end of operator.
• «\Qq{//div[@id="abc"]}\E» isn't valid Perl code, but it's expected to be when using the «e» modifier.

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It might be best to split out the replacement.

my $repl = '//div[@id="abc"]';

s/.../$repl/
[download]

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The following would also work:

s{...}{ q{//div[@id="abc"]} }e
[download]

s{...}{ '//div[@id="abc"]' }e
[download]

Changed the delimiter to allow «\» to be used unescaped, and removed «\Q\E».

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If you change the replacement expression's delimiter to «'», it will act as a single-quoted string literal instead of a double-quoted string literal.

s{...}'//div[@id="abc"]'
[download]

Probably best to avoid this one because it's pretty obscure.

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