First, I'd stay away from the square. Lots of people (especially in the design/fashion profession) try to do non-standard business cards, to show how creative and "outside the box" they are. It's become a cliche.
There are Flickr pools and online galleries devoted to unusual business cards, and some of them are admittedly clever. But many of them are just "different to be different" and annoying to those who receive them. I think that's where you're square falls, to be honest. Basically, if you're going to go with a nonstandard business card, you had better have a damn good reason - and just wanting a unique shape isn't.
You say you might keep the square design for your tags. I would consider going the other way - maybe making your business cards look like your tags? They both contain the same information, to a point, and that would allow you to give your business card some visual interest and uniqueness (a punched hole, trimmed corners) while still fitting inside a standard business card holder.
Second, your color palette. You say you love pink - and I do too - but it really registers as red on a computer monitor, and red, black, and white is pretty much the harshest color combination I can think of. Unless you're Target, an ambulance, or the White Stripes, it should usually be avoided at all costs. I haven't seen your fashions - I don't know if they're similarly bold, and that's what you're going for - but I do know an age-old adage for design that still holds true today: If you want to make something look more expensive, soften the palette. When you think of your archetypical perfume box from a high-end brand, it's probably not red, white, and black.
Again, I don't know if expensive is what you're going for, or not. These are just my thoughts - take them or leave them. But I would at least try using a lighter pink, and see where it takes you. If you decide you hate it, it's okay.
A final word: Take the compliments to your website to heart, and then look at your business card. The reason everyone loves your website (or the reason I do, at least) is because it's so simple. It's understated. It doesn't have competing fonts or diagonal text - and that's why it works. Keep that in mind while you finalize your business cards, and good luck!