In real life the " Oleson's" surname was Owens. The father "Nels" was William H Owens, the mother "Harriet" was Margaret H, the children were Nellie Owens, and William "Willie" Owens. By 1880 The Ingalls had moved to their permanent residence in Dakota Territory and Nellie was only 10 years old so it is unlikely she eloped with anyone While the Ingalls were there in the 1870's, as Nellie would have been under 10 years of age at the time.
Miss "Eva Beadle" was actually Mrs. Clementia Bedal. (the name was sometimes mispronounced Beadle. It was not permitted back in those days for married women to teach school, thus the "Miss". In real life Clementia's husband Lafayette Bedal and his father Elias Bedal took out a plat on the land and formed the town of Walnut Grove. Laura Ingalls father Charles was the first justice of the Peace. There was an Eva Bedal, she was the oldest daughter of Lafayette and Clementia but she was born in 1870 and younger then Laura. ( By the way, Clementia was my grand aunt.) Clementia remained married to Lafayette until his death in 1881 in Aitkin county, Minnesota and never married a Simms.
The name of the main street through Walnut Grove is Bedal street to this day, named after Lafayette and his father.