iOS 13 on iPod Touch 7th generation
Source:


  The supported device for iOS 13 as follows:
  
  
  iPhone 11
  iPhone 11 Pro
  iPhone 11 Pro Max
  iPhone XS
  iPhone XS Max
  iPhone XR
  iPhone X
  iPhone 8
  iPhone 8 Plus
  iPhone 7
  iPhone 7 Plus
  iPhone 6s
  iPhone 6s Plus
  iPhone SE
  iPod touch (7th generation)**
  


But checking the fine print with ** for the iPod touch states that it won’t be available on the iPod touch until the 24th or 25th of September (depending on your location).

Your best bet is probably to try installing a developer beta or a public beta.