I would like to know if it is possible to send an Heirloom from a character I have in Icecrown to one in Lordaeron. I know that it is not possible between different expansions, but I don't know if it can be done between kingdoms with the same expansion without having to move the character as is.
You're trying to compare someone supporting the server - so you play for free - and getting some gear, with you "being smart" by getting stuff fast to use on a slow server. Even if there was no such discrepancy, the answer would still be no, because that's not how Heirlooms worked on WotLK anyway.