Yes it’s a real word, and used correctly. All verbs (except defective ones) can be made into verbal nouns by adding -ing (after removing any silent “e”). This is called the gerund. As an inflected form, it will not necessarily have its own dictionary entry.

As Phil said, it's a real word and it's used correctly. We have the preposition "beyond" and prepositions take noun or gerund phrases. Imagining is a gerund and gerund phrases can include a determiner and an object. beyond [noun or gerund] beyond imagining [correct] beyond our imagining [correct]

I think that you're right that "beyond our imagination(s)", or "beyond our ability to imagine" are more common terms than "beyond our imagining". However it can be used this way. A quick search brings up a quote from one of Cormac McCarthy's screenplays. "But nothing is crueler than a coward, and the slaughter to come is probably beyond our imagining".

I think.... "our imagining" is incorrect, you have to say "our imagination". Imagining is a verb. It is mostly used when talking about objects. For example: If Donna saw a ghost or a person walk past but John didn't see it he would say, "You are imagining things, Donna!". Hope this helps! :)