When a disaster strikes, off duty personnel will be called in and be on site in a few minutes - unless there's some for of Disaster preventing people travelling the ship and Worf has to become a midwife, but then patients wouldn't be able to get to sickbay anyway.
I suspect you're unlikely to need any more than a single nurse overnight, and only if you've got patients in sickbay (which seems unlikely). In the UK there is about 1 hospital bed for every 500 people, meaning about 2 people in sickbay on average, but the enterprise has fewer old people who need more hospital treatment, no bed blocking, better in-quarters monitoring, as well as more advanced healthcare. Most of the time nobody would be an inpatient, the rest of the time the doctor is just a few minutes away.
You'd need two doctors on a ship without an EMH in case one of them needs a doctor, or one dies on an away team, but sickbay actually seems the right sort of scale for a ship with about 1000 people on board. That theres only 1000 people on board a ship that size is a whole separate issue.