There's clearly different opinions on this. To me, a really big factor seems to be which doll manufacturer the doll is coming from. From what I've read here on ODC, the vast majority can send you a new doll within a couple months... you can see where I'm going with this... Then with Sinthetics, it can be a couple years. Rachel arrived here about 5-6 months after she was poured, but from what others have written, it sounds like it could be as much as a year!
If all the doll makers were consistent in their wait times, I'd probably side with their birthday being the day they're popped from the mold ... BUT another consideration is every doll coming out of that mold looks identical and not the doll ordered so maybe we should consider their birthday isn't until all the custom features are applied and they actually become YOUR made-to-order doll.
With all that being said, it seems as if shipping day or arrival day would be most realistic. To me, there is NOTHING more exciting or mind blowing than arrival day... I'm going with Arrival Day... With that, my Rachel is a ripe old age of 16 months!