I have recently been employed by a nursing agency. The agency is asking that I attend manual handling education before commencing work. Is it my responsibility to source this education?

The Work Health and Safety Act 2011 outlines the duty of care held by an employer. Under the act your employer has a duty to ensure you are provided with the training and instruction to protect you from risk that can arise from the workplace. So, if it is mandatory your employer should be providing you with the training.