I would say "a doctor", unless you want to specify "her doctor" (dokternya) or our "doctor" (dokter kami). And "chosen" might be a better choice of words, instead of "picked".
Agree that chosen is more tone appropriate, but picked is acceptable.
"picked by doctor" is unambiguously wrong.
also, just a note for the course administrators...
i am marked incorrect if i type in 'mum', and told the correct word as 'mom'. it is only one letter different, but here it is treating my answer as incorrect, rather than as just a typo.
'mom' is american english. in australia, new zealand and england it's 'mum'. please, it would be great if you could add 'mum' to your database as well :)
Interesting, cos I've surprisingly been marked correct on a lot of sentences for using "Mum", despite being marked incorrect for all manner of other bad reasons.
"The mother's food is chosen by a doctor" should be accepted, shouldn't it?
I chose this form because nothing here seems to suggest that it is my mother, rather somebody's mother.