Using a regex saved in an environment variable

J0ax88 has asked for the wisdom of the Perl Monks concerning the following question:

I want to use a regular expression stored in an environment variable. I have this one-liner that works fine without using an environment variable:

perl -00 -ne 'print if /--Begin--/ && /--End--/' file.txt
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file.txt contains:

Hello World

--Begin--
Cat
and
Dog
--End--

other stuff 
This is a test
Good Bye
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The above one-liner prints out what I want:

--Begin--
Cat
and
Dog
--End--
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Now I want to do the same thing except put the regular expression in an environment variable:

export REX="/--Begin--/ && /--End--/"
echo $REX
/--Begin--/ && /--End--/
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So I tried doing this:

perl -00 -ne 'BEGIN {$rex = $ENV{REX}} print if qr($rex)' file.txt
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and also this:

perl -00 -ne 'BEGIN {$rex = qr($ENV{REX})} print if $rex' file.txt
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But it always prints out the whole file. Any help would be appreciated.