Thanks for the clarification… it does change things slightly if you have not already bought your pet.
If you have a Body Corporate Manager then perhaps you should contact the Manager and get him/her to chase up the other Committee member who has not yet responded. I am pretty sure the Committee member would be contactable by email and/or by phone. Their response must be in writing though.
Has the one person who has responded given their approval? If they have then you may be able to work through them to contact the other member and get their approval.
If only one person out of two responds (i.e. if one member refuses to respond) then the VOC is ‘lost’ (i.e. not Passed). You could advise the Manager and/or the Committee that the Committee cannot unreasonably refuse your application and that you will be seeking an Order from the Tribunal if they do not give you permission to keep a pet.
Having only 2 people on the Committee is not particularly workable. Are you able to and do you want to get yourself on to the Committee?