Hi bonniegirl
Welcome to TS!
You really need to pay a visit to New Register House in Edinburgh, or get someone to do that for you.
"Doreen" as a name is probably (I've been proved wrong before now!) relatively unusual so that finding the birth of Doreen FINDLAY should be a matter of a few minutes scanning the annual birth index for the likely period concerned.
Assuming that the birth can be found, it's then a matter of tracing forward to see if there's a marriage record or death record in Scotland. If there is a marriage record, then looking for children, and so on.
There's also a shortcut that
might be worth a try. From 1974 onwards the death indexes also show the maiden name of the mother of the deceased. In other words, in this case, you would look for any death record where the registered surname is FINDLAY and the name in the column showing the mother's maiden name is GUNN. It shouldn't matter if it's a married female involved as there will most often be entries under both married and maiden surname of the deceased.
Have you also traced forward the other brother William Alexander FINDLAY ?
Partly because of experience of the difficulties, - not least time and cost - involved in tracing forward in the records in England and Wales, it's often not realised that tracing forward in Scotland is perfectly straightforward, and, SMITHs and the like apart

, shouldn't take too much time or cost that much. Even for SMITHs, it's only a matter of a bit more time.
Starting from a late 1800s record, it should be possible to find some recent addresses for living relatives in a day's research, always assuming, of course, that there are such relatives.
The biggest problem can often be getting male lines past WWI. Once the tree can be brought forward to the first couple of decades of the 20th C, then it's just a matter of time to find any Scottish records that there are.
Despite my joking comment above, SMITH or similar can be just a quick
if there is use of middle names, otherwise it just adds on up to a couple of days.
David