Jeff, the rally location is Taree, on the mid north coast of NSW.
The laptop has become an essential part of most rally participant's kit, along with one or more GPS devices. Generally the waypoints are given out in digital format eg on a USB data stick and the computer is needed to then manipulate the waypoints to create the rider's route. Software such as Garmin BaseCamp, Garmin MapSource (no longer updated by Garmin), TYRE, Steets and Trips (in USA), MS excel and others are options for the routing. Many rallies still offer plain text data so that paper maps can still be used, but that is on the decline. I think that Annette and Shane are using this training rally with a clear future in mind of Aussie rallies that start and finish in the same location and require routing to be done 'on the clock' at some time during the event.
I'm no tech person. I don't know if a tablet is a good choice though, unless it accept the data and it can run the required software for you to plan a route.
I doubt very much that turning up to a rally with just a phone (desktop is still back at home on the desktop of course) would be a good idea. One of the key techniques in successful rally routing has to be the ability to 'see' a winning route among the coloured dots and lines of the map. The small screen of a phone would be pretty cluttered.
As for computers they don't have to be fancy. I personally run a 5 year old lightweight 13inch HP Ultrabook (solid state drive to give some protection against road knocks) and Windows 7. BaseCamp runs just fine on that and that is all I use for routing.
It is always difficult when starting out on a new activity to anticipate just how 'into it' you may become. That can lead to some underpreparation I think (eg getting by with a phone for GPS and a dozen paper maps). That underpreparation may then result in much more stress and difficulty and then much less enjoyment on what should otherwise have been a fun event ie riding around some great roads and seeing places you never thought you would. On the otherhand, picking up a laptop and some form of routing GPS (maybe a phone can do that - I don't know) and spending some time getting used to them over the next couple of months should provide a better opportunity to see what rallying is all about.