A sentence straight from Itazura no Kiss anime, episode 4 (last few minutes):
Aitsu ga itteta na, tensai ga itsu kedamono ni naru (no) ka wakaranai tte sa.
Lit. He was saying, you don't know when a genius will become a beast.
The focus now is on the boldfaced phrase.
I've heard questions nominalized without the "no の" -- that's why I put it in parentheses. Sample sentences in jisho.org also do not use の when nominalizing a question. However, Masahiro Tanimori's Handbook of Japanese Grammar uses the の. My guess is that both are correct, with the のconstruction as more formal (although I've never heard it before). Also, note the use of "ga が" instead of "wa は", since this is a subordinate clause.
Another example is this sentence construction:
Tanaka-san ga kuru ka dou ka shitte imasu ka.
Lit. Do you know whether Mr. Tanaka will come or not?
The "かどうか" construction here means "whether or not".