Sounds like a good opportunity to publish your app on cpan that way regardless of OS, Perl version/vendor users could install it and the dependencies by something like:

cpan App::MicrocebusCoolAppNameHere
[download]

The corelist command shows when a module first became core, and you can also find out which version of the module came with which perl:

C:\Users\mmcgrath>corelist -a File::Find

Data for 2015-09-12
File::Find was first released with perl 5
  5          undef
  5.001      undef
  5.002      undef
  5.00307    undef
  5.004      undef
  5.00405    undef
  5.005      undef
  5.00503    undef
  5.00504    undef
  v5.6.0     undef
  v5.6.1     undef
  v5.6.2     undef
  v5.7.3     1.04
  v5.8.0     1.04
  v5.8.1     1.05
  v5.8.2     1.05
  v5.8.3     1.06
  v5.8.4     1.07
  v5.8.5     1.07
  v5.8.6     1.07
  v5.8.7     1.09
  v5.8.8     1.10
  v5.8.9     1.13
  v5.9.0     1.05
  v5.9.1     1.07
  v5.9.2     1.09
  v5.9.3     1.10
  v5.9.4     1.11
  v5.9.5     1.11
  v5.10.0    1.12
  v5.10.1    1.14
  v5.11.0    1.14
  v5.11.1    1.14
  v5.11.2    1.14
  v5.11.3    1.15
  v5.11.4    1.15
  v5.11.5    1.15
  v5.12.0    1.15
  v5.12.1    1.15
  v5.12.2    1.15
  v5.12.3    1.15
  v5.12.4    1.15
  v5.12.5    1.15
  v5.13.0    1.15
  v5.13.1    1.16
  v5.13.2    1.16
  v5.13.3    1.17
  v5.13.4    1.17
  v5.13.5    1.17
  v5.13.6    1.18
  v5.13.7    1.18
  v5.13.8    1.18
  v5.13.9    1.19
  v5.13.10   1.19
  v5.13.11   1.19
  v5.14.0    1.19
  v5.14.1    1.19
  v5.14.2    1.19
  v5.14.3    1.19
  v5.14.4    1.19
  v5.15.0    1.19
  v5.15.1    1.20
  v5.15.2    1.20
  v5.15.3    1.20
  v5.15.4    1.20
  v5.15.5    1.20
  v5.15.6    1.20
  v5.15.7    1.20
  v5.15.8    1.20
  v5.15.9    1.20
  v5.16.0    1.20
  v5.16.1    1.20
  v5.16.2    1.20
  v5.16.3    1.20
  v5.17.0    1.21
  v5.17.1    1.21
  v5.17.2    1.21
  v5.17.3    1.21
  v5.17.4    1.22
  v5.17.5    1.22
  v5.17.6    1.23
  v5.17.7    1.23
  v5.17.8    1.23
  v5.17.9    1.23
  v5.17.10   1.23
  v5.17.11   1.23
  v5.18.0    1.23
  v5.18.1    1.23
  v5.18.2    1.23
  v5.18.3    1.23
  v5.18.4    1.23
  v5.19.0    1.23
  v5.19.1    1.24
  v5.19.2    1.24
  v5.19.3    1.24
  v5.19.4    1.25
  v5.19.5    1.25
  v5.19.6    1.26
  v5.19.7    1.26
  v5.19.8    1.26
  v5.19.9    1.26
  v5.19.10   1.27
  v5.19.11   1.27
  v5.20.0    1.27
  v5.20.1    1.27
  v5.20.2    1.27
  v5.20.3    1.27
  v5.21.0    1.27
  v5.21.1    1.27
  v5.21.2    1.27
  v5.21.3    1.27
  v5.21.4    1.28
  v5.21.5    1.29
  v5.21.6    1.29
  v5.21.7    1.29
  v5.21.8    1.29
  v5.21.9    1.29
  v5.21.10   1.29
  v5.21.11   1.29
  v5.22.0    1.29
  v5.23.0    1.29
  v5.23.1    1.29
  v5.23.2    1.30
[download]

I'm unaware of a similar method for finding out what additional modules come with different perl distributions, likely you'd have to trawl through lots of documentation/history, and this isn't practical. Be aware that some OS also ship cut down versions of perl, without certain modules, another good reason for managing dependencies via a cpan release.