The best way to do that right now is to embed a Google Form into your InDesign document.

  1. Open a form in Google Forms.
  2. In the top right, click Send.
  3. At the top of the window, click Embed Embed.
  4. To copy the HTML that appears, click Copy or press Ctrl + c (Windows) or ⌘ + c (Mac) on your keyboard.
  5. Paste the HTML into your website or blog.

Then use Object > Insert HTML to insert the embed code into your InDesign document.

If you don't actually need to submit the data, but you want to get the appearance of a submit action, check out the tec