Does the shimmy come through the steering wheel, happen at any other times, like when turning sharp to the left? If it doesn't come through the steering wheel, it wont be being caused by the suspension/wheel.
Jack up the right front tire, and see if there is any movement, then use jack stands and see if the a-arms move around w/o any weight on them.
If you are new to Toy's, first gear isn't a granny gear, so as long as it doesn't pick up speed like the clutch is in/trans in neutral, you are probably fine.