I'm not sure a Security specialist would really be needed. I mean, this is a very small group of people. If somebody began acting out of line, this would not, could not be handled by a small group of specialists breaking out weapons and subduing the miscreant; odds are that there would be way more mutineers than "security", or that a high percentage of "security" would be mutineers. In a small boat, the team would just have to be self-regulating.
If the crew is to undertake planetside heroics, it's again a job for the entire dirty dozen led by their regular CO and XO, not specialists. There just isn't critical mass for anything else.
In terms of allocation of personnel resources, I only see two needs: keeping the ship flying, and wrangling science out of the places where the ship goes. A crew of half engineers, half scientists would make sense, with at most one person dedicated to command duties; if there was any need for commanding when he or she was asleep, a bit of wakey-wakey would be perfectly practical. Sawbones and weapons could be side jobs for the scientists or wise versa, considering the automation no doubt available in the 23rd century.
On the issue of running the ship around the clock, this might actually not be a requirement. Quite possibly, 90% of the star hours would be clocked in ferry flight with most sensor or weapons systems shut down; if anything happened en route to the mission target, the tiny scout would ignore it, or at most vector in some other Starfleet asset.