I sell many parasols on ebay. Have sold some small ones. The one you show in the photo may have a folding handle, it is hard to tell.
I would keep checking the ebay auctions. Search antique parasol. The problem you will have is there are many reproduction parasols listed with the title, "antique parasol".
Another problem is the tops are often torn. I sell them with torn tops and people have new tops made for them. So keep checking the auctions. This week alone I will be listing two small parasols.
You are also going to need to have a measurement on hand. I list the total length and then list the measurement across the top, the underneath of the top.
Good luck, you should be able to find one on ebay but it might need a new top.