The book is a children’s book, found in Denmark in 1965, possibly originally Japanese, if so then published somewhat earlier.
A tiny Scotsman encounters Nessie the Loch Ness Monster. Far from being afraid be becomes her friend and calls her “Wee Beastie.”
There’s a book call “Loch” by Paul Zindel from 1994 where the father encounters a character like the Loch Ness monster but a baby that is named Wee Beastie I believe. I know that’s not the correct time frame but thought I would mention it just in case.