Grete Janus Hertz was a Danish children's author (1915 - 2002). Originally published in Danish as 'Nar Lisa och Lena Hade Rode Hund', and translated and published in English in 1965 (my copy is from 1975).
The story is of two 7 year old twin girls who have measles and the mischief they get up to whilst they should be resting in bed! The illustrations and colours are lovely.
I've never met anyone else who had this book as a child - let me know if you did.