I think, since you're opening the file for write, that trying to read it in isn't really going to work. If you run it with warnings, as a standalone file, you're more liable to see that this:

#!/usr/bin/perl -w
open(INIT, ">doit");
while (<INIT>) {
    printf "%s\n", $_;
}
close INIT;
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when run gives:

    Filehandle INIT opened only for output at init.cgi line 3.

How about this for an even shorter solution? -- since Perl reads the entire file into memory before compilation, by runtime, the file is no longer necessary.  Hence, you can do it like this:

#!/usr/bin/perl -w
unlink $0;              # Delete myself!

print "Still here!\n";  # Prove that script executes okay
# Rest of code follows ...
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Now:

    % init.cgi
    Still here!
    % ls init.cgi
    ls: init.cgi: No such file or directory