Where possible you should provide all of your evidence together, however if you will not be able to get the proof of further / higher education before your evidence deadline you should provide the rest of your evidence and with a covering letter confirming you do not yet have the further / higher education proof.
Your application will be processed but your child / sibling will not be taken into account during the initial assessment.
Once you have the proof of further / higher education you should submit a change of circumstances to add a dependant child / sibling and provide the relevant supporting evidence.