Since undead are a lot more productive than humanhumans (24/7) the only thing humanhumans will be needed for are the body. As such the empress should find ways to improve the birth rate of her new country. To allow a quick increase in the birth rate food will have to be abundant.
Also, the mortality rate is probably nowhere near what she will need to maintain a zombie horde in good condition. She will need to increase it or bring in corpses from neighbouring country by trade or military.
To prevent unrest, rebellion or massive emigration the people need to know that they are safe and that tomorrow they will not be the next zombie. There are many ways to go about it. One way that could be interesting is to use a caste system. The "normal" human would be free to live their life except that each family would have to give a newborn to the other caste. These ones are to be turned into a zombie when they turn 18 or 20. The members of that caste are probably taken care of by their own family, or it could be an adoptive one, because they represent safety for the rest of the family.
You might want to read about Amonkhet (a world in Magic the Gatheringgame Magic the Gathering). They use mummies with treated bandage and the desert keeps the zombie dry, which helphelps explain how they are not ridden with diseases and infections for the living population (very important for the agriculture).
There is always the option of using something else than a normal zombie such as a mix of a vampire and a zombie. Zombies could be feedfed blood to slow down the rotting process which, would keep the population weaker, while allowing the military and work force to last longer.