There is no legal requirement to have a pest inspection done, however not undertaking a pest inspection can prove to be a false economy in the long run.
If the Committee are not willing to undertake an annual pest inspection then you have the option of raising a Motion at a General Meeting requiring that an annual pest inspection be undertaken. The Motion would require approval by Ordinary Resolution. You could obtain a quote from a reputable pest inspection company and include it in your Motion.
A termite inspection, and an annual treatment for cockroaches on common property would be two common actions undertaken by an OC.
Not all termite damage is the responsibility of the OC as the duty to repair and maintain is not limitless: <i> Mullen v Owners Corporation SP15342 [2017] NSWCATCD</i>
Below is a link to a Tenancy site that deals with who is responsible for pest infestations. Some pests would not be responsibility of the OC, unless they are on common property. Black or brown ants, and cockroaches are two examples where the owner or the tenant would be responsible for ridding their individual Lot of these pests as the general cleanliness of the inhabitants could be all, or partly, to blame for such an infestation in a Lot.
https://www.fairtrading.nsw.gov.au/housing-and-property/renting/during-a-tenancy/pests-and-vermin