She studied botany, zoology, mathematics and physics at the universities of Münster, Innsbruck and Göttingen, earning a master's degree in 1958 and a PhD in 1960.
[1] In 1969, she completed her habilitation in Münster; her thesis was titled Die Feinstruktur vegetativer Flechtenthalli nach Untersuchungen mit dem Durchstrahlungs- und Oberflächen-Rastermikroskop ("Fine structure of vegetative lichen thalli investigated with scanning electron microscopy and transmission electron microscopy").
One of her best-known publications was a chapter on fine structure in The Lichens (a popular 1973 textbook edited by Vernon Ahmadjian and Mason E. Hale).
In 1986, Peveling organized "Progress and Problems in Lichenology in the Eighties", a scientific conference held in Münster.
[2] In his survey of influential lichenologists, Ingvar Kärnefelt called her "a fore-runner in that she succeeded in a scientific career and reached the highest academic rank in Germany during a time when women rarely even tried to compete for such positions".