It would depend on what she was crossed with. If it was another dairy breed, then probably about 6#/day.
I don't know of any way to predict what will come from the cross. IMO, genetics is a calculated guess/risk. We try to learn as much as we can, so that we can try to stack the odds in our favor. But you are never sure what you will get until it is mature and milking.
Your doe is truly an "unknown factor." You don't know her genetic background, so there is no way to "predict" what she will milk, let alone what her offspring will milk.
From what I have heard, if she is out of an Alpine crossed with a meat breed, then you are not very likely to get very good milk production out of her.......and her offspring are not likely to be good milkers either. The other factor in milk production is how long does she maintain her level of production? Does she peak at 10# one month into her lactation.....and then decrease so that she is dry 4 months into her lactation? IMO, it is much better to have her peak at 8# and still have her producing 6# 9-10 months later.
Once in a while, a buck will be very dominant in what he produces, but that is very, very rare. Usually it is just a combination of the sire and dam......and the generations behind them. (That is why some people like to have "papers" with the goats that they buy. After all, it costs just as much to feed and keep a goat that produces very little as it does to feed and keep a good producing goat.)
Just my thoughts.................