Hi superman-jj, and a warm welcome to the forums! 🙂
Here's a workaround...
Create a new folder called say Web, drag any browser URLs you want to that folder, rename them as you wish, do a Get Info on them one at a time, highlight the small icon at top, paste and previously copied Icon you wish, close Get info windoe, do next one, then drag that Web folder to the right side of the Dock between Applications & Trash... you should have a pop-up menu of your links. 🙂