The first thing I'd note for those interested in doing this for themselves, Blood Elves are the only race other than Forsaken that starts at friendly with the Undercity. In my case, this made things much easier from the word go. Now, I could have run over to the Forsaken starting area and done quests there from level one on up, but I really didn't want to miss out on the rep rewards with Tranquillien. So in my case, I leveled from 1-20 with Tranquillien, then bounced around doing content here and there until level 38, at which point I settled into the rep grind in earnest.
Starting in the Forsaken newbie area, I tore through the quests from Deathknell to Tarren Mill in easy stages over a few days. (For anyone who has a serious session planned, this can easily be done in a day at level 38, but that blasted real-life thing kept me popping AFK.) I originally intended to try to get to exalted solo, without instancing. Sadly, I wound up about 6k shy at the end, despite having run every arc across the level 1-39 content that I could find that would give Forsaken rep. So I headed to the instances, and chased down every ounce of Forsaken quest rep from Ragefire Chasm to Scarlet Monastery. Sure enough, that last bit of instancing put me over the top. I also managed to make most of the two levels I needed in running around and completing these quests so that when the time came, I was only about 1000xp from level 40. A few kills later, and I was ready to go.
From there it was simply a run back to Brill to get my Little Undead Pony. Thus, a cross-faction mount by no later than 40 via non-holiday regular questing can definitely be done. In the case of Blood Elves and Forsaken, it will require not only chasing all non-instance rep that you can get in the old world, but also at least one run through each of the lower instances to get quest completions as well. (Although I will say that at 38, you can easily stealth run Razorfen Kraul as a Rogue to get the drop for Going, Going, Guano, and I'd imagine Druids would be able to as well.) For races that don't start as friendly to one another, I'd imagine it would be harder to attain by 40, but with the rep available in other instances like Uldaman, Zul'Farrak, and Razorfen Downs, it shouldn't be too terribly difficult to attain shortly thereafter.
Have any of you managed Exalted with a different faction by level 40 just because you wanted that cross-faction mount as your first one? (Or perhaps, you disliked your racial mount that much!) Any tips or tricks that you could give to others looking to get a cross-faction mount by level 40?