Howdy, emm3e. 

I can get this fixed for you in no time. Normally the tax codes that would show up in the drop-down list varies on the selected transaction.  

For example, an expense transaction will show the rates for GST Purchases, while a sales transaction displays both Sales and Purchases.

In order to show the GST rate you've set up, let's check to see if it's active in the settings.

Here are the steps: 

1. On the left panel, click GST. 
2. Click the Settings drop-down menu located in the upper right-hand corner.
3. Choose Edit Rates.
4. In the GST page, click the Gear icon above the Action column.
5. Put a check mark on the Include Inactive box.
6. If the rate is turned off, click the Toggle icon to turn it on. 

You can check this article for your future reference: Check how much GST you owe in QuickBooks Online. 

I'm always at your side if you still need my help. Stay safe!