The way GST works in most countries, is that you must remit it yourself. Uber will not do this for you as you are an independent contractor.
For example, I am in Canada.
If Uber pays me $10.50 for my share of a trip, 50 cents of that is the GST at our current 5% rate. So, in the case of my arrangement with our tax agency, I remit my GST once a year, after deducting the GST I had to pay on everything I purchased for driving Uber. Gas, cell phone, accounting, car washes, maintenance, insurance, etc, etc.
Last year I received about $3,000 of GST from Uber, and paid about $1,800 back to the government.