Summarize:

To make wooden gears, you should have access to a wood work studio. You'll need access to a band saw or jigsaw, an awl, brad point drill bits (5/16 or 8mm), and a wood rasp. You'll also need access to a printer, a smooth shank, and short wood screws. You'll need to use Baltic birch plywood because it is very durable. You'll recognize this type of plywood based on the several layers within the wood. You could alternatively use UHMW plastic, Masonite, or phenolic resin material. Avoid using spruce or fir plywood because it is simply not strong enough. When handling this type of equipment it may be wise to use some safety precautions. First, never allow a young child to operate any large machinery unsupervised. Though it is not required, wear safety glasses while operating the larger machines. There's a chance of a small scrap of wood to pierce your eye. Go online to a free wood generator like  https://woodgears.ca/gear_cutting/template.html for your template. A generator like this allows you to modify all the aspects like tooth spacing, number of teeth, number of spokes and more. When you've created the right sized gears, print them off.  Templates generally have two different sized gears. The template will allow you to make size adjustments without messing up the gear ratio. The template is designed to adjust both large and small gears together. The teeth will be the same size for both sized gears to ensure a smooth rotation.  Generators like this even let you animate your design to test how it works. There are more sophisticated gear templates that are available for download as well. You can also create your own template using paper, pencil, and a protractor.
Receive access to a workshop. Gather the right plywood. Use safety supplies. Obtain a template.