"I saw her while walking around."
Translation:Dolaşırken onu gördüm.
You have to put onu after dolaşırken if you want to mean that you saw her, him, or it. I don't think that "onu dolaşmak" makes sense. Does it? I think "ben onu dolaşırken gördüm" might mean "While I was walking around him/him/it, I saw". Anyway, even if it did, that isn't the right translation of the sentence.