The following sentence (in a context which is speaking about a woman):
青いワンピースを着て、どこに行くんだろう。
Can be translated as:
Where is she going in a blue dress?
Could I use「かな?」instead of the「ーだろう」form? E.g.:
青いワンピースを着て、どこに行きますかな。
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Sign up to join this community青いワンピースを着て、どこに行きますかな。
doesn't sound natural (at least in modern standard Japanese), I'm afraid. The polite form of 「~だろう」 is 「~でしょう」. (行きます is the polite form of 行く, as you may know.)
青いワンピースを着て、どこに行くのでしょう。/ 行くんでしょう。
"I wonder where (she) is going in a blue dress."
Using かな, you can say:
青いワンピースを着て、どこに行くのかな。
This would mean almost the same thing as your original sentence.