The aircraft was being operated on a Permit to Fly pending issue of a Certificate of Airworthiness, and was being ferried to Coolangatta for avionics maintenance and to be statically displayed at an airshow. The pilot reported that after a normal landing on runway 35 in a 12 knot crosswind, he encountered slight nosewheel shimmy and the nosegear collapsed almost immediately. A tubular engine mount frame, which supports the left hand trunnion bearing block, had failed. This allowed the left hand trunnion to become dislocated and the nosegear collapsed. Excessive nosewheel shimmy had been reported on a previous occasion. The nosewheel shimmy-damper washers had been lubricated. This may have reduced their effectiveness leading to excessive nosewheel shimmy and possible damage to the tubular frame.