You need to consider whipping less. Emergencies only. Or at least have a damned good reason to whip.
You are better off growing to the happiness limit, and then turning off growth by emphasizing production and creating specialists.
I'll whip if I fear losing a wonder, or really need a given unit or improvement absolutely right now ... or I'll do it when losing to screw with my enemy, but I won't do it lightly.
Another thing Dom will do, if the opportunity presents itself, is grab a neighbor's capital early. If you can do a Quecha, Impi, or Skirmisher rush early, and grab a capital city at size 3 or 4, you will be way ahead ... In fact, it is easily worth making 6 or so Quechas, and just over-running someone's capital before 3000BC.