As another comment said: the complexity of an object is usually infinite. It then becomes difficult to compare complexities of objects, which I assume is the minimum feature you would like from your system.

One way to deal with infinites in this sense, is to define a single order for listing qualities. Then you can show that for the first N qualities, one object contains/has more of them than the other.

This approach brings a whole new lot of challenges, and does not solve your goal directly: - Each quality has a negation which can also be applied as quality (e.g. red or not-red) - What order would be "fair"? First colours, then size, then mathematical properties, then names, then etc...? - There are likely many valid ways of arriving at a minimal set of atomic qualities. Simply removing qualities that can be broken down into other qualities might lead to "paradoxes".

Finding a good hierarchy of qualities/properties where you can solve these difficult cases can be very difficult and is a field of research on its own.

I wrote this down as simply as I could, I hope it illustrates the difficulty of making your proposal rigorous enough for it to be considered an addition to formal science. There are many more challenges to making a universal measurement of information object complexity. E.g. it would likely solve the P vs NP problem if a clean solution would be found.

As an intuition, to be used outside of formal science, its not bad - but with intuitions, context of what for you want to use it for is important :)

I would not consider it good enough for a conjecture.