I don't think that a mortality rate for newborns of 48% is very realistic. With it that high (and given the other asumptions) I had to set the doe harvest rate relatively low or the population would go into a rapid decline.

Anyway, after making a lot of initial assumptions and in answer to your question a 20% harvest rate for antlerless deer would begin to stabilize this scenario after about 6 years. At that point the population would be in a very gradual decline and one might want to tweek the harvest rates at that point.

Note the spike in Doe:Buck ratios in year 1. This is due to initially starting with only 18 month old buck in the population. Because there were no button buck in year 0 the antlered deer that were either harvested or died post season were not replaced. If this was a real situation where there truly were no button buck in the population I would not allow the killing of any antlered deer the first year and then put a longer term plan in place but because this is just hypothetical and not very realistic at that, I didn't bother.