Is $6,000 to add a 2nd zone to a 2-story home's HVAC system a fair price?

We have a 2-story home with a finished basement. Our current HVAC system is 2-stage but only has one zone. The second floor struggles to get cool in the summer, particularly our baby's nursery which has lower ceilings and stays warm. We are seeking estimates and opinions on adding a second zone or installing mini splits upstairs to address this issue. Our wallet prefers the 2nd zone option, but we have concerns about its effectiveness and the required work in the finished basement. We have 3 bedrooms upstairs. We are told our current system is properly sized for the house but doesn't work effectively with just one zone. Our primary concern is regulating the temperature in the nursery bedroom.