Most books can be dated fairly easily from their imprint information, usually found on the verso (the back) of the title page – in addition to the publisher, there is often the date or some other indication of the edition or impression of that particular book.
Unfortunately, Walter Crane is one of those authors / illustrators whose works are particularly difficult to date, and “ Baby’s Opera” seems to be no exception. Many of the editions (especially the pre-1900 editions) are undated.
The British Library online catalogues are not particularly helpful because of this, and they don’t even offer a clue as to when Warne took over the publishing rights. Neither does there seem to be any detailed online bibliography of Crane’s works.
The 2 main printed bibliographies are Masse, Gertrude C. E. A Bibliography of First Editions of Books Illustrated by Walter Crane. London : Chelsea Publishing, 1923 and Spencer, Isobel. Walter Crane. New York : Macmillan Publishing, 1975, and between them they almost certainly offer as much detailed information as to editions, bindings, points of issue etc. as you will find anywhere. Sadly, I don’t have either bibliography to hand to be able to help you.
The chances are, though, that ‘your’ copy of “Baby’s Opera… is more-or-less contemporary with the inscription date.