Both mine started out with a dairy sensitivity. I breastfed both, and did not re-introduce dairy into my diet until after they were weaned (one at 12 months, one at 17 months).
I tried them both with whole milk in a cup at age 1. At that time, my first child was fine - he had outgrown it. My second child - we were up all night with a crying baby, poor little guy. We waited another 6 months, and at 18 months we tried Lactaid milk (the ped's recommendation) - we were up crying all night again. So now we are waiting again. We'll try again sometime after he turns 2. My conclusion is that some outgrow it, some don't.
And, I would strongly encourage you NOT to put dairy back into your diet until you've tested the baby at age one with some milk in a cup. Because, as you know, it can take several days for the dairy to work it's way back out of your system. If the baby is still sensitive to it, he'll be suffering for several days while this happens. If you try milk in a cup and he's still sensitive, you can go back to breastfeeding immediately and he has something safe and comforting to drink while his tummy recovers.
Also, in the long view - I'm so glad that your planning to nurse until at least 15 months. Again, if she is still sensitive to dairy at age 1, the longer you nurse, the better it is for her because that is much healthier than soy or rice milk in a cup. They are ok alternatives (my son drinks rice milk now and he's thin but healthy), but they do not have the good healthy fat content that breastmilk and whole cow's milk have. So keep up the nursing as long as you can, and especially while you wait out the sensitivity. Good luck!