I assume you mean "Jewellery through security" as there is no scanning outbound by Customs.
The outbound passenger security screening is looking for possible dangerous good or potential weapons. So unless your engagement ring resembles a weapon, it should not cause any issues at the security screening point.
You may also be entitled to claim the GST cost back under the Tourist Reimbursement Scheme (TRS), but that requires you taking the item and receipt to the TRS desk after security screen at an international terminal, which may not be easy for you if you want to keep it a secret. Note conditions apply regarding eligibility of the TRS.


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