Birthday Cake in Venice?

I think I'd just go to a pasticceria and buy one that looks good out of the case and pack along a box of tiny candles in your bag. You might also consider purchasing an assortment of Italian yummies so that everyone can sample a bit of them?

Just as a start, Pasticceria Tonolo sees very good reviews, and there's a few snaps of their cakes on their FB site. It's possible if contacted in advance that they'd decorate one but then you wouldn't have the advantage of picking what you think she'd like from the offerings.

https://www.facebook.com/pg/PasticceriaTonolo/photos/?ref=page_internal

https://www.tripadvisor.com/Attraction_Review-g187870-d2362934-Reviews-Pasticceria_Tonolo-Venice_Veneto.html

Google Maps or hotel staff could help a pasticceria closest to your hotel, so you don't get lost trying to accomplish this. Majer has several locations in Venice (open daily) and mentions cake, but a specialty item could be expensive. When I happened to pass Nono Colussi one year near my hotel off Piazza San Barnaba, one thing I liked about them was that they featured a different, freshly-baked item in the window every day (cookies, etc., closed Mon-Tues). A Sunday or Monday closed day is common.

If you shop at Conad City grocery store and you see a pastry counter, if they sell cake slices they will also sell you whole cakes. If you don't see whole cakes on display, tell them you want to buy a whole cake and they'll bring it out for you. That's where I buy my cakes.

And they have a great candy section where you can buy all kinds of chocolates and other goodies. Chocolate is must cheaper in Italy.

I do not know if you will have a day or so lead time - but if so you could order a cake from this bakery - excellent quality. Perhaps you could email them and order it from them.
Bar pasticceria Ballarin

web site
http://pasticceria-ballarin.it