You dont have much choice but to use the Brown Mountain road RobnMaz. Its steep, expect to be in low gear and going slowly. Lots of caravans and trucks use it.
Its a nice drive from Bega up Brown mountain, so have a go first without the caravan. Have lunch at the Nimmitabel pie shop before returning and enjoying the view at Pipers lookout on your way down. Big landslides are pretty rare, and have happened after heavy rain. If the weathers been fine you'll feel better.
RobnMaz we just pulled our van up it on Monday. The landslide section is finished but as they are putting the final touches to it they have traffic lights on it. Looks like they have done a good job with it. We just took it steady (our van is only 14' pulled by Nissan Xtrail) and had no problems - even when a truck in front loaded with a bulldozer was unable to make it around the last corner in the 'work' section we were able to get past it and move on. It's not a long climb and there are only a few 25km bends. You should be right. If you've got the time Gerty's suggestion is an interesting one but it would increase your mileage. All the best from a gusty cold Bowral!!