The plural suffixes in Klingon are optional. Qelpu' is explicitly plural and cannot be read as singular. Qel without the -pu' suffix could possibly mean that it is one doctor or more than one doctor. Context will usually make it clear (like when you have already been talking about a specific doctor or multiple doctors or the sentence uses a prefix that can only be used for a singular or plural). In conversation you can always ask for clarification if it doesn't seem clear.
This course often lacks any helpful context, so both answers are usually accepted. If one answer had been Qel and another answer had been just Qelpu', I'm sure the software would have accepted either as correct.
The Qelpu'vetlh'e' answer is wrong because the -vetlh suffix makes the phrase into "those doctors".
Other parts of the sentence (or of the discussion) might make the use of the plural redundant. Or lack of other indicators in the sentence (or discussion) may make it bad style to mean plural, but leave off the suffix. However, the grammar has the plural suffixes being completely optional in all but a couple rare circumstances.