Barbie dolls:
Dressing up Barbie dolls is probably best fit for very young girls. There are many fantasy-like dresses available that leave room for lots of imagination. You won't find any designer kids clothes here, though.
Fashion Board Games/Designer Sets:
Most fashion board games are about fashion knowledge (like the game called "Fashion"). This might be interesting for a bit older girls that are very enthusiastic fashionistas. Dress-up board games are actually quite rare and the only one I know of is called "Pretty Pretty Princess". So, unless you really want your daughter to be playing a board game, you shouldn't be searching for too long in the board game section for a dress-up game.
There are, on the other hand, many designer sets out there for many different age groups. Designer sets provide your child with the utensils necessary to design several pieces of garment. While certainly a fun activity that will teach your daughter more than just dressing up, it isn't suited to be trying out different brand clothes.
Online Games:
As you have probably already expected, this is the game type where dress-up games with children designer clothes can be played. Dress-Up games (and other fashion games) are abounding on the internet. One website I know of for example is http://www.dressupgames.com.
An interesting fact, though, is that these games usually let your daughter dress up women designer clothes for adults; and not designer clothes for kids. Nevertheless, online games provide the best way to play dress-up games. It's the only way to provide your daughter with lots of clothes to try on (since they only have to exist virtually).
A real designer kids clothes simulation does not exist (or not that I know of). Most online shops are trying hard to present their designer kids clothes as vividly as possible, but there are no dress-up games on their websites.
I hope that after having read this short article you will be able to find lots of good games for your daughter where she can play dress-up games. Kids are supposed to learn a lot through games in their early age. So who knows, maybe turns out your daughter has a flair for fashion. She might then be able to use her dress-up game experiences to succeed in a fashion career.

