onliness
/ˈəʊnlɪnɪs/(also onlyness)
noun
1The fact or condition of being alone; solitariness, solitude.
2The fact or quality of being the only one of a kind; singularity, uniqueness; specifically the fact of being an only child.
Origin
Late Middle English; earliest use found in The Wycliffite Bible (later version). From only + -ness.