Hi Bill
> I've had a couple good-sized Australian Pine trees (US name) come down in my
> yard recently in S Florida.  I believe the trees are known as She-Oak in
> Australia and that they are not related to pines at all.

Correct.  The species you have in Florida is Casuarina equisetifolia, 
and there is some information about it here:

https://bie.ala.org.au/species/http://id.biodiversity.org.au/node/apni/2911837

It is a tropical and subtropical species, generally found on coastal sites.

> The wood is more
> dense and has a reddish color.  Does anyone have experience with using the
> wood for projects?  Wondering about its workability, how it takes stains, if
> there are special drying considerations or other considerations.

C. equisetifolia doesn't grow here in Tasmania where I live, though 
there are other Casuarina species here.  Examples of the Tasmanian 
species rarely grow large enough to do much with other than small boxes, 
turned pens and egg cups etc. Most of trees large enough to consider 
sawing have deeply fissured and folded trunks, so that it is difficult 
to get slabs or sawn pieces which do not have bark inclusions.  The 
pieces I have played with work well, though the timber is very hard and 
sharp edges are essential.  Depending on how the log has been sawn there 
will be medullary rays as in US oak.  In my experience boards are 
difficult to season without warping, cupping, twisting and splitting, 
but that may be because the source trees were slow-grown on hard sites, 
so probably had plenty of internal stresses to relieve!

Casuarina makes great firewood, though splitting the logs is hard work.  
It burns very hot, and local wisdom is that burning Casuarina regularly 
in a slow combustion heater will risk burning out the firebox.

If Derek Cohen is on the porch at the moment he will probably have more 
useful information: I have seen some quite long and wide Casuarina 
boards sourced from Western Australia where Derek lives.

Regards,

Tony B
Hobart, Tasmania