From what I understood on your post, your family is not here in Doha.
If your family is not here then you cannot extend the visa as it requires them (at least your wife) to get medical test from Medical Commission.
If this is the case then you just have to apply a new visit visa for them.
As for the question if you can apply immediately or wait for 3 months, I do not know because in your case the previous visa was unused so I am not sure if the 3-month rule applies.
From what I understood on your post, your family is not here in Doha.
If your family is not here then you cannot extend the visa as it requires them (at least your wife) to get medical test from Medical Commission.
If this is the case then you just have to apply a new visit visa for them.
As for the question if you can apply immediately or wait for 3 months, I do not know because in your case the previous visa was unused so I am not sure if the 3-month rule applies.