(으)ㄹ까 하다

I ran across this grammar point in my Integrated Korean - Beginning 2 textbook. Not riveting or anything but I would like to try it out. It essentially means "I am thinking of doing such-and-such" or "I might do such-and-such"

It seems this verb stem is used to show the speaker's intent in the future. If you are not exactly sure what you're going to do, then this verb stem is appropriate. That is how it differs from (으)ㄹ게요. Some examples:

A: 피곤해보예요. 괜찮니? You look tired. You okay?
B: 그래? 오늘 일찍 잘까 해요. Really? I'll probably go to bed early (tonight).

A: 비 와서 우산 살까 해요 Since it's raining, I might buy an umbrella (but maybe not)

A: 날씨 더워서 좀 이따가 샤워할까 해요 Since the weather's hot, in a little bit I might take a shower.

A: 저녁에 뭐 할 거예요? what're you going to do tonight?
B: 집에서 영화이나 불까 해요  I'm thinking about watching a movie