It depends what you mean by designer shopping. Are you looking for full-price or discounted?
For discounted stuff, your best bet is probably the Premium Outlets. Check
here for a list of stores. From Old Town, travel west on the US192 until you hit the I-4 and then take that east (towards Orlando) leaving at exit 68. As you come up the exit ramp, you'll hit a fairly big, light-controlled intersection. You need to head straight across. As you reach the other side, you'll have Little Lake Bryan on your right and Bahama Breeze on your left. Keep going for about a mile, past the Mary Queen of the Universe Shrine, and the entrance will be on your right.
If you want the proper stuff, you definitely want to head to Mall at Millenia which is just north of Universal Studios. It's an upscale mall boasting the likes of Jimmy Choo, Tiffany & Co, Chanel, Louis Vuitton, Burberry, Gucci, Dior, Juicy Couture and Cartier amongst its tenants, as well as Bloomingdale's, Macy's and Neiman Marcus. It also has some great places to eat. Again, from Old Town, head west on the 192 to the I-4 and take it east, leaving at exit 78, Conroy Road. At the top of the ramp, turn right and then right again at the next light, followed immediately by a left into the parking lot. In fact, there are several entrances, so don't worry if you miss the first. You'll be able to see the mall as you exit the I-4.