A children's picture book, ca 1965, in which a tiny Scotsman meets the Loch Ness Monster, Nessie, and becomes her friend and calls her "Wee Beastie". Does it ring any bells?
The book could be Ted Hughes' children's book "Nessie the Mannerless Monster", which was published in 1964. The picture book has lovely illustrations by Gerald Rose. You can find pictures of book cover and illustration by googling, but here you can find a couple of photos: