I have been unable to find a book entitled Sensible Susan in the catalogues of the British Library, WorldCat or the Library of Congress. Due to the alliteration in the name, it is also possible that "Sensible Susan" refers to a stereotype that figures in a specific book and that the characters in Nesbit's The New Treasure Seekers are referring to the book by means of that character rather than the book's title.
Alice Nuttall's article The Susan: The Story of an Archetype, and Why We Need Her (19 November 2018) seems to support the assumption that "sensible Susan" may be a stereotype (emphasis mine):
Are you the eldest girl in a classic children’s novel? Are you extremely sensible and organised? Do you have a younger sister who’s a bit of a tomboy, and who all the readers love more? Then you might be a Susan.
If you’re reading children’s literature from a certain era, a Susan is bound to pop up sooner or later. She will be the second child, and the oldest girl. She will always be the group mum, keeping her siblings in line and standing in for their actual mum, who is always absent and sometimes dead. She will make sure that her brothers and sister are fed, clothed, and have somewhere warm to sleep. They will not appreciate her for doing so.
Unfortunately, the examples given in that article come from more recent books than The New Treasure Seekers:
- Susan Walker from Arthur Ransome's Swallows and Amazons (1930),
- Susan Pevensie from C. S. Lewis's The Chronicles of Narnia (1950–1956),
- several characters whose name isn't even Susan but who are "Susans in nature, if not in name", including … Dora Bastable from E. Nesbit's The Story of the Treasure Seekers.
Arthur Ransome's The Picts and the Martyrs (1943) at one point refers to Susan Walker as "sensible Susan" (emphasis mine):
Dorothea read her letter aloud, a pleasant cheerful letter from their mother, hoping that they would both have a happy time at Beckfoot, hoping that the new boat was ready, and that they would presently be teaching her and their father how to sail, urging them not to take risks at first, and saying that she was really rather glad that while that sensible Susan was not there to look after things they would be sleeping in a house and not miles from anywhere in tents on an island or up in the hills.
Later on, she is also referred to as "the careful Susan" (emphasis mine):
Then, remembering the careful Susan, Dorothea began to plan her housekeeping, and set out, on another page, to make lists of food for separate meals, breakfasts, dinners and suppers.
The stereotype is also mentioned in Maria Nikolajeva's book chapter "The Identification Fallacy: Perspective and Subjectivity in Children's Literature" in Telling Children's Stories: Narrative Theory and Children's Literature, edited by Mike Cadden. University of Nebraska Press, 2010):
Instead of portraying one complex character, the author splits the personality between several actors, getting the brave Peter, the sensible Susan, the treacherous Edmund, and the honest Lucy rather than one character possessing many and sometimes contradictory features.
(The list obviously refers to characters from The Lion, the Witch and the Wardrobe, but the discussion is more general.)
In a snippet view of Delphi Complete Novels of Frances Hodgson Burnett (Illustrated) (Delphi Classics, 2014), I found:
The reader learns to love sensible Susan Sowerby, Dickon, the animalcharmer, Ben Weatherstaff, and the dear, pert little robin.
Susan Sowerby is a character from The Secret Garden, which was serialised in 1910–1911, several years after The New Treasure Seekers (1904).
Below are a few examples of "sensible Susan" from before 1904.
In "Uncle Sam's Daughters" in The Plantation (1872):
There is the sound, sensible Susan, who with her clear-cut face, watchful, moderate eye and well-chosen dress fills up the corners at hop or ball, where conversation does not prevail. Susan is too sound and practical not to know that marriage is her just and fitting career; and to know, too, within a fraction, how much love and income will be requisite to make the aforesaid marriage move upon well-oiled wheels.
In The Haunted Room by Charlotte Maria Tucker (1876):
"On windy nights, I suppose," said the sensible Susan. "I've heard a sighing, and a rattling, and a howling even here in Summer Villa."
In Miss Priscilla Hunter, and My Daughter Susan (1879):
"What a blessed comfort a quiet, domestic, elderly daughter must be; fashioned like that sensible Susan of Mrs. Carleton's!"
This I said to my husband one evening, (…)
In Marriage à-la-mode, Volume 2 (1880):
I never thought he would have been attracted by any of my girls, except my sensible Susan.
In After many days; or The turning point in James Power's life (1882):
Thus sensible Susan found work for her brother-in-law.