早点 means breakfast in Chinese, I've heard of it from time to time, I live in Chongqing, a southwest city of China. People here don't use the word much, we say "早饭", but, in 东北，northeastern part of China, people do say 早点， as in "你吃早点了吗"? (Have you eaten your breakfast?) Also, I believe people in Beijing use it, too.
FYI, 早点 also could mean "come earlier than usual", as in "你能早点来吗？" Would you please come here earlier?
To Beijingers, 早点/早餐 sounds a bit more "elegant" than 早饭, and 早饭 would be the most “homely” among three.
点 originally refers to 点心 like small cakes. They may or may not be on the actual breakfast menu.
早餐 "a generic term for breakfast": 早晨的餐食 (e.g., anything from McDonald's breakfast menu).
早飯 literally "morning meal": 早晨的餐飯 (e.g., a full breakfast or a breakfast meal to fill up the stomach, last night's leftover, food eaten out of shared dishes, homemade breakfast such as rice porridge with side dishes).
早點 literally "morning snack": 早晨的餐點 (e.g., morning high tea, a champagne breakfast, beverage and confections, specialty foods and delicacies, manufactured foods such as 麵包、燒餅、油條 purchased at a food stand or a store).