All examples I've seen on the internet refer with this phrase to money. But isn't it possible to club together with, for instance, our group effort/our knowledge and experience/our part of work?
'Club together' specifically refers to splitting the cost of something between a group of people - it is not used for other divisions of resources or labour.
A term with the broader definition that you are looking for would be 'pool our resources', which can be applied to more than just money.
'put our heads together' would be more suited to knowledge or ideas - a group of people might put their heads together to solve a difficult problem, for example.
According to the Oxford English Dictionary (subscription required), club together means
To combine in making up a sum (as the cost or expense of an entertainment, etc.) by a number of individual contributions; to go shares in the cost of anything.
To contribute (as one's share) towards a common stock.
I don't think either of those necessarily requires the cost to be in money. For example, one of the quotations is,
T. Smollett Roderick Random I. xxiii. 212, “This scheme, towards the execution of which my companion clubbed her wardrobe.”
That's not specifically "club together", but I don't see any reason why we couldn't, for example, club together to provide a donation of clothes to charity from our wardrobes.
Indeed, "club" itself has plenty of meanings, such as
To combine together (or with others) in joint action; to combine as partners or as members of a club.
So, again, it seems reasonable to "club together" in the joint action of using our collective knowledge to solve some problem.