I assume you mean in the context of other sentences so I'll restrain myself from commenting on the intepretation, 'Your son or doctor?' ;) I agree, although, they are about as similar as 'sock' and 'shock'.
Come to think of it, I've encountered (Portuguese) folk mishearing 'doctor' as 'daughter' in English. I think that 'daughter' may have it's origins in defunct English mutation (cf. think, thought) so it might come from 'dau(c)k' + 'ter' and have been pronounced close to either the Dutch word.
Nup, apparently, 'daughter' has only occured with the '-ter' suffix since as far back as Proto-Indo-Iranian but I can't find what the 'daugh-' cognate in PII would mean. '-tr-' is probably some kind of grammatical declension.
The computer voice is pretty accurate, the w is not very outspoken, but it is pronounced. You can find more examples here: http://www.heardutchhere.net/DutchPronunciation.html#UW