What recourse do I have if my company's senior management and the audit committee are not supportive of having an external QA performed and thus will not approve the funding required?

There are alternatives that may assist you in obtaining an external QA. For example, contact your local chapter to determine if they can assist you with an independent validation conducted at minimal cost to your company, other than maybe travel costs if the validator does not live in your city. Another option is to conduct a peer review with other local internal audit activities, rotating the assessment among members of the group, and must include at least three members. If management and the audit committee are not supportive, then your efforts at educating them regarding the reasons, benefits, and overall approach to an external QA are needed. IIA reference materials are available to help you in this effort (free in most cases to IIA members). Additionally, work with your external auditor to educate the audit committee on the benefits of an external QA, which may include additional reliance on the internal audit activity's work. This could result in making the overall external audit more efficient and effective.