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This is a topic we have addressed previously on another thread on this topic:
http://eu.battle.net/wow/en/forum/topic/1498672093?page=3#52After a bit of investigation, it seems that though sending heirlooms across realms might well be something we'd like to consider doing at some point, there's currently no immediate plans to make the necessary changes to allow this to be possible.
This is not, as some claim in this thread, because we're wanting to encourage people to use paid Character Transfers to be able to transfer heirlooms to characters on other realms. It's unfortunate that this remains the only way players can achieve this and we would like to look into possibly changing this once priorities and schedules allow.
In the meantime, however, the generally reasonable length of time needed to level up through the newly remade lower level zones (especially if combined with guild perks and the extra experience boost you can get from running through dungeons as well) should be more than sufficient to get your characters on other realms to a higher level without an unreasonable investment of time, and probably also with a decent portion of fun.