This may be a new feature but you can now add a link to a heading (right click pick link then click heading and scroll down to the relevant one)

Not sure it works exactly equivalent to Word's feature but it's something.

Disclaimer: This is the official account of Docx2Latex

We have just launched a Google Docs-add on which combines the power of LaTeX and ease of word processors and cross-referencing too.

Here are the features provided by Docx2Latex add-On

1. Write LaTeX code snippets inside Google Docs with syntax highlighting.
2. Add captions to figures and tables.
3. Cross-refer figures and tables.
4. Auto update captions and references when a new figure or a table is inserted.
5. View LaTeX compiled to PDF in real-time.
6. Automatic LaTeX source code generation and downloading.

Add-On Link: Docx2Latex Google Docs Add-on

Watch Demo: Short Demo

Let's say you want to add a link to chapter 10 in table of contents (TOC).

Step 1 . Go to chapter 10. Select title, Select Insert option in menu. Insert bookmark.

Step 2. Go to table of contents page. Select text referring to chapter 10. From the menu, select Insert. Insert Link. Then select Bookmarks from the new menu that appears. Selcet bookmark specific to chapter 10. Done!

You can also edit the link text.

You can apply similar method to cross-reference images.

I think the most similar way to achieve this is to create a bookmark and reference it whenever need it.

• Insert bookmark before Table 1.

  Bookmark can be inserted from menu Insert > Bookmark

• Go to the place where you want to refer Table 1

• Type "Table 1", and select it to insert a link
• Collapse Bookmark in the link dialog and select Table 1

This is not ideal, after all you have to type "Table 1" twice. But it does allow user to navigate within the document. Therefore somehow similar to cross reference.

Short answer

At this time Google Docs doesn't have the cross-reference feature.

Explanation

The above is based on my personal experience with Google Docs and that there is nothing relevant to cross-reference features on the official documentation. To find the official documentation, go the link on the references section.

References

Google Docs editors Help