A horse's gestation period Is 11 to 12 months. Though they are slow to show being pregnant, a horse within several months of foaling would be obviously pregnant, which this horse is not.
Mercury thermometers take quite a bit of time to equilibrate for accurate temperature readings, longer than shown in this episode.
A search of the Australian on-line historical newspaper archive (Trove) reveals that the phrase "in the scheme of things" was in use from at least 1909 onwards (possibly earlier) so it is not anachronistic for Tristram to use the phrase in the period of 1938.
In the final scene, Tristan suggests that he and James should "get blasted" at The Drovers. "Blasted" was first used as a euphemism for drunk or high in 1972 according to etymonline.com.
Tristram says 'in the scheme of things'.
Doubtful that this use of phrase was current in 1938.