Pegasus Airlines Child Ticket Policy Leaves Parents Frustrated

I got screwed over by Pegasus Airlines. Our flight is scheduled for a day when our baby will be two and a half years old. I made a ticket request because the system doesn't allow children over 2 years old on the flight date. But, it's causing problems. I heard that choosing a ticket for a child under 2 years old might cause issues on the day of the flight. What do people typically do with kids in this age group? Do they have the ability to fly? I've called customer service four times, but they still haven't figured out a solution. People say that once the child is 2 years old, they can join the flight if there's room. If there isn't enough room, I suppose I'll have to leave my two-and-a-half-year-old child at home. I feel like I'm being treated unfairly.