I found one source that claims 14 to 18 months for long-lasting memory, though without defining "long-lasting".
Remembering comes on various levels, though:
Daddy turned to page 134.
Daddy read me The Phantom Tollbooth
Daddy read me stories
I loved my time with daddy
Ask yourself this: Why will your child remember what you look like?
The answer is, of course, that seeing you was a repeated experience, but that is not all... the emotion behind each of those experiences gives them added strength/meaning/weight.
My daughter remembers me reading her The Phantom Tollbooth, but none of the other books -- it was one that for whatever reason embedded in her permanent consciousness... and that is how long term memory works... it is sometimes rather random. Where there is strong emotion, though, there is an increased chance of the memory lasting longer.
The point is that you really shouldn't care about what she will or will not remember to varying degrees -- just make every moment count and their sum will carry the day in that she will remember you for the awesome parent you are, in all its various facets.