In England in the early 19th century, most girls and women wore a mob cap or bonnet when they were indoors. These might be made of cotton, muslin or lace.
Later on in the century, it was usually only elderly ladies who wore bonnets indoors. However, servants continued to wear mob caps when working until the end of the 19th century.
It is not clear whether the situation was the same in other countries in Europe. However, we can get some idea from 19th century European paintings: A Dutch painting of 1880 shows middle-aged ladies wearing indoor bonnets; a Swiss painting of children having breakfast, dated 1879, shows all but one of the girls wearing mob caps.