ND Ilirija , 1920. The colours were red and white.

The country which we now know as Slovenia was a part of the Austro-Hungarian Empire. As we have seen, football gained a great deal of popularity in this region at the turn of the 19th to 20th centuries. At this time the city of  Ljubljana was undergoing a revival, being modernized following a destructive earthquake. In the first decade of the 20th century 'English Football', as it was known locally, became a very popular activity in the city's educational establishments. 

A Slovenian football website has this group labelled as Hermes (1910), so it looks as if  ND Ilirija took on the club colours after their merger.

In 1910 the club Hermes was formed by students in  Ljubljana. The members were Slovenes and the club had strong associations with Slovenian nationalism. ND Ilirija  was founded in 1911 (in classical times this region of the Balkans was known as Illyria).  At first Ilirija  were streets behind Hermes, losing one of their esrliest encounters 18-0.
1913 was a significant year in the development of Slovenian football. Hermes and ND Ilirija  had been coverging slowly- Hermes providing   Ilirija with a venue, practice facilities, balls and even, increasingly, players.  in 1913 the clubs merged.

 ND Slovan (1913)
1913 also saw the foundation of  ND Slovan as the city's second major team.

August 5, 1913. ND Ilirija  0, Slavia Prague 10

Most important of all though was the visit to Ljubljana of  Slavia Prague. Slavia unsurprisingly thumped Ilirija 10-0, but it gave the Slovenes insight into the potential of a well drilled football team. Slavia's Jaroslav Jirkovský (who had experienced international football with Bohemia, a forerunner of Czechoslovakia)  stayed on in Ljubljana, taking charge of ND Ilirija .
The Balkans were at the centre of the 1914-18 war, so it is hardly surprising that there wqas not much football activity during these years. From 1919 Slovenia was pat of The Kingdom of Serbs, Croats and Slovenes.
Football prospered after the war, with clubs emerging throughout Slovenia. In 1920 a regional football association,
 Ljubljanska nogometna podzveza, was formed. This was a branch of the national governing body. A Slovenian representative side was also formed, losing 5-0 to France. 
On the national scene two Slovenian players represented Yugoslavia.
full-back Stanko Tavčar (ND Ilirija ) appeared at the 1920 Olympics. Goalkeeper  Maksimilijan (Maks) Mihelčič, who began his career with Hermes but  for most of his career played for HSK Gradanski Zagreb, represented Yugoslavia 18 times, including at the 1928 Olympics.
Slovenian clubs made little impact on the Yugoslavian national championships. ND Ilirija  competed in the years 1923-1927. In the first 4 editions, which were cup competitions, they didn't make it past the 1st round, and in 1927, when a league system was introduced, they finished bottom of the 6 team table.
On the domestic front ND Ilirija  were dominant. The regional championship was introduced in 1920.
The list of champions reads:

1920: ND Ilirija 
1920/21: ND Ilirija 
1921/22: ND Ilirija 
1922/23: ND Ilirija 
1923/24: ND Ilirija 
1924/25: ND Ilirija 
1925/26: ND Ilirija 
1926/27: ND Ilirija 
1927/28: ASK Primorje 
1928/29: ASK Primorje 
1929/30: ND Ilirija 
1930/31: I.SSK Maribor
1931/32: ND Ilirija
1932/33: I.SSK Maribor
1933/34: ND Ilirija
1934/35: ND Ilirija
1935/36: SK Ljubljana
1936/37: SK Železničar Maribor

ASK Primorje- founded in 1920, a Ljubljana based club that merged with ND Ilirija in 1935 to become SK Ljubljana.
SSK Maribor- First Slovenian Sports Klub Maribor- a multisport club based in Slovenia's second largest cirty, founded in 1919.
NK Železničar Maribor another Maribor club, formed by the railway workers.