Of course by now you are aware that Yugoslavia did not exist until after WW I !Croatia, however has been in existance since 925AD and Karlovac has been part of Croatia since beofr that time.In 1907 Croatia was under the rule of the Austro-Hungarian Crown.
Also Fannie is not a name that would be found in Croatia.
Is this your family as found in the 1920 Sugar Creek MO census?
Name Age Andrew Stavlenitch 38 immigrated 1903 Helen Stavlenitch 36 immigrated 1907 Frank Stavlenitch 15 immigrated 1907 John Stavlenitch 12 Katie Stavlenitch 10 Mike Stavlenitch 9 Mike Stavlenitch 7 Nick Stavlenitch 1 [1 8/12]
However Andrew's ship manifest concurs with your immigration date of 1907
Name: Andro Stavljenic Arrival Date: 19 Mar 1907 Birth Year: abt 1884 Last Residence: Recica (east of Karlovac City) Birth Location : Mackuze (which is really Donje Mekušje, located in Karlovac County a bit south of Karlovac City) Age: 23 Gender: Male Race: Croatian Port of Departure: Rotterdam Port of Arrival: New York, New York Ship Name: Statendam
Have searched high and low for mother and son... to no avail