Great timing, Apophis! I only just received the answer to this inquiry moments ago. Currently it's not possible to obtain the Exalted status necessary to obtain another race's mount. The development team realizes that this is a problem and are actively working on adding faction quest content that can be repeated by players, similar to what exists for the Argent Dawn factional quests.

Please keep in mind that the faction currently being gained will still be useful when the said changes have been implimted, as players will be that much closer to hitting the Exalted mark.
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Online Community Representative