"Dob the pill" (Child's phrase)

In some British private schools the phrase "dob the pill" is a request that someone should throw the ball to you. The Internet is almost completely silent on this phrase with the only use I can find in the first comment at http://www.adelaidenow.com.au/sport/afl/pieces-of-the-power-puzzle/story-fn83zjlm-1226049635520 where it says "With his build Ebert would be a better back pocket where he could dob the pill deep over centre.".

What is the origin of this phrase?

It's not a phrase but informal English. According to the ODE, "dob" means:

ORIGIN 1950s: figurative use of dialect dob ‘put down abruptly’, later ‘throw something at a target’.

And pill, according to the same source, means

3 informal, dated (in some sports) a humorous term for a ball.

Now if put together, it'd simply mean throw the ball.