Surely Daniel must have been already born in 1977 when Eloise shot his future self. Otherwise he would have been a professor at Oxford University before the age of 19, which is hugely unlikely. (Desmond visited him in 1996 and he was a professor).
So this raises the possibility that perhaps he was born on the Island. However, the fact he did not get a nose bleed like many others during the time flashes suggests otherwise. Therefore, maybe Eloise gave birth to Daniel whilst off the Island and then returned without him.
What do you think?