I use Degei, which has nice automation for setting up IDs for clutches.
Once set up, it produces whatever ID numbers you want: Mine go something like 'WWP-BP-11-01', 'WWP-BP-11-02', etc.
It doesn't allow you to automatically create IDs that include morph or gender, but you can also choose to set up the records manually if you want.
I take care of the rest of by naming the animal after its sire and dam, morph and gender, and then ID number (which would be 'o1', or '02', etc). So, the animal with the ID 'WWP-BP-11-01' would be named 'KalikaXAnansi_NormFem_01'
Really, how you choose to ID your animals is entirely up to you, there's no system everyone uses.