If you ever Google for parasols, you will find that the majority of the top results are stores selling garden parasols. An eBay search gets you the variety that only fit babies' prams - and of course, plenty of items that are not parasols. Stores selling parasols sized for the adult human to carry are quite difficult to find. Luckily, my bookmarks contain a few websites that I have been previously recommended, so when I was asked if I could suggest any, I could supply some links immediately. Also, I searched Etsy. How on earth did we survive before Etsy?
Brollies Galore have got the Chinese paper variety, Edwardian parasols, lace parasols and frilly Can-Can parasols. The prices range widely as well, so you can get very pretty cheap ones or if you want to splash out you can get some expensive extravagant madness! They are based in the UK but they ship worldwide. The Black Rose have a black and white polka dot parasol on their website (worldwide shipping) and more at their Camden store.
Victoriana.com have a page that lists antique and vintage parasols in eBay auctions. There are a range of varieties, and as you might expect, a range of prices. You can also order their Amazon Drygoods general catalogue which includes parasols. The Oriental Trading Company do a small selection including one in white lace and some paper paint-your-own parasols. They ship to the USA and Canada.
From Etsy I would suggest Umbrella Heaven, and if you have Cash To Flash or just want to look, Darna's East Angel Harbor Hat Shoppe has a few absolutely extraordinary Victorian-style parasols. They are too over-the-top for my taste (all that lace and all those bows!) but I can still appreciate the work that goes into them, as I am sure you will too.
If you want to do it yourself, here are some instructions for converting an umbrella into a parasol, thanks to that bastion of style advice, the alt.gothic.fashion FAQ.
My only parasol is one my parents got me from Disney World when I was two and a half - it's pink and minimally frilly, and has my name written on it. Obviously this makes it practically perfect in every way - Mary Poppins reference intended - and so maybe I can live without Loretta!