I am impressed that this module is not installed

You should add it as a dependency to your Makefile.PL, as you should with all your dependencies (see ExtUtils::MakeMaker):

use ExtUtils::MakeMaker 6.64;
WriteMakefile(
    ...
    PREREQ_PM => {
         # your module's runtime dependencies
    },
    TEST_REQUIRES => {
        'Test::Exception' => 0,
    },
);
[download]

I assumed that by default this is a core module and it would be installed by default but I guess I was wrong.

It is not a core module, as you can check with corelist:

$ corelist "/Test::Exception/"
/Test::Exception/  has no match in CORE (or so I think)
[download]

Does any one know any other way of testing croak?

Personally I use Test::Fatal, but I think Test::Exception is a good choice too.

use Test::More;
use Test::Fatal 'exception';
like exception {
   die "Blam";
}, qr/\bBlam\b/, 'exception is as expected';
[download]

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