All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Separation of boys and girls at schools and universities should be observed at the age of puberty, since co-education leads to immeasurable and unlimited forms of evil and harm. However, it is better to observe separation at the age of discretion; i.e. 7 years.
In other words, it is better and safer to make children accustomed to this Islamic rule and it is needed to avoid unveiling the ‘Awrah (what is between the knee and navel for men and the whole body for women). This, in turn, constitutes a big step on the correct adherence to the teachings of Islam and good morals.
As for before the age of discretion, there is no harm in mixing between males and females for the Prophetic Hadeeth that reads: “Command your children to pray when they become seven years old, and beat them for it (for not praying) when they become ten years old; and separate between them in beds.” [Abu Daawood]
Then, know that there are particular signs to the age of puberty. For more benefit, please refer to Fataawa 85089 and 83431.
As a result, there is no harm in establishing such a club as long as you adhere to the above-stated standards.
For more benefit, please refer to Fataawa 341845 and 357337.
Allah knows best.