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According to the 1806 regulations, an Austrian Uhlan regiment consisted of four divisions, each of which consisted of two squadrons (see below, Exercir-Reglement ..., p.3). Each squadron had 128 Gemeine (troopers) (ibid., p.10f.). Of these, 16 were armed with short carbines instead of with lances (ibid., p.5; in this instance, the carbines are called "Feuergewehr"). All lancers (or all troopers?) had a pair of pistols, and sabres, of course.
However, according to Ottenfeld, who is referring to the 1798 regulations, two complete divisions were armed with carbines, the other two with lances. Just one pistol. Didn't check whether that's correct. If so, things must have changed between 1798 and 1806(?).
Everything about the Austrian cavalry can be found in two manuals, dated 1806, the first of which primarily is concerned with unit composition and manoeuvres ...
The falling plume - although said to have been introduced only after the Napoleonic Wars - seems to have been used already before, as this watercolour by Johann Adam Klein proves (inscription - "Klein fecit Wien 1814 bei dem Einzug des Kaisers") ...
As for the pistol holsters. They were hidden for the greater part below the shabraque and fur but on the Klein picture you can see the lower end of the holster protruding from under the shabraque, and the upper end of the butt from under the fur. So shabraque and fur must have been perforated.