Is it really necessary to buy a plane ticket for my daughter? She will be under 2.?

I don't have the money to buy my daughter a plane ticket for a seat and since she is under 2 (shes 21 months for be 2 in sept.) its not required that i buy her one. And last time i flew i always had a seat next to me open in fact they made sure i had a seat for her just in case of an emergency and I'd need the oxygen mask. I fly from SEA (Seattle- Tacoma, Wa) to RAP (Rapid city, SD). Last time there was a ton of turbulence which scared me but everything turned out okay. I didn't take my carseat but this time around i would take just her cosco carseat from wallmart. I'm just wondering if it is "REALLY" necessary to buy a seat.