My native Japanese friend said that both どうかな and どうなんだろう can be translated as "I"m not sure". Do they actually mean the exact same thing? Or are there subtle differences in their usage?
どうなんだろう is more explicit about the fact that the speaker is unsure and wondering about something. どうかな can be used in broader situations.
どうかな tends to be used when the speaker knows the answer:
A 「どうだった？ テストは合格だった？」
B 「さあ、どうかな？」 (≒ "Hehe, guess what.")
And compare the two sentences:
Both どうかな and どうだろう basically translate to "what do you think?" here, but in the former sentence the speaker is confident and expecting a positive reaction, while in the latter sentence the speaker is unsure and asking for a listener's opinion.
They mean the same, your japanese friend is right.