Hi Snoop,
The Prom circuit is lovely. I've walked it a number of times over the years, including a winter solo in 132km/h winds*. On that particular occasion there weren't any hikers after Waterloo Bay (I did it in reverse to the typical route). Of all spots in the Prom, this is arguably the safest to go solo. You'd certainly find it doable, but it takes a bit of motivation to keep slugging in poor weather between Waterloo and the Lighthouse. You also will probably want to review your gear and abilities beforehand. If things go pearshaped it is purely up to you to get out of the situation
In terms of campsites, they are all pretty safe if past experiences are anything to go by. Roaring Meg is a nicer campsite to Halfway Hut, but if alone I'd opt for the latter as it is much quieter in the evenings (probably avoid the hut, there used to be a snake under it). Refuge and Little Waterloo bays are both beautiful, and usually have a few campers there even at this time of year.
There are some nice picture spots between the two, as well as between Refuge and Sealers, and a couple on the NW side of the Lighthouse.
Hope you enjoy the experience and stay safe and warm.
Tim
* Before this descends into a debate about the merits and/or safety of solo hiking, these winds were on one windy night that was considerably rougher than forecast. My trip plans would probably have differed if this was predicted in advance. Nevertheless, I was equipped for the conditions, had appropriate plans for if things went pear shaped and thoroughly enjoyed the experience (which was brought on by the sudden injury, pre-trip, of my planned walking mate). There is a time and place for the practice, but obviously it requires considerations beyond those that group walks typically encompass.