This is a good chance to teach your daughter in a far better way than that mother is teaching hers. That mother is teaching her daughter not to think for herself, not to be satisfied, not to be curious, not to be happy, but only to imitate, be jealous and only do what someone else has already thought of.
So sit down and talk to your daughter. Tell her there will ALWAYS - whether she becomes a teacher, a stay-at-home-mom, an astronaut, a writer, a Nobel Prize winner, a clerk in a store, a chef, a computer technician, or a fashion designer - be people who will be jealous, will be mean-spirited, will copy her and who will not be able to think for themselves, and there will also be people who inspire her, encourage her, teach her, help her, and remain loyal to her. Those are the important people to think about and learn from. The others are just the result of living on a crowded planet.
Tell her that now is a good time to think about how to respond to all the people your daughter will meet (teachers, a future spouse, her favorite authors or tv characters, friends, parents of friends, doctors, neighbors). Ask her to start thinking: is this person helping me? Can I learn good things from him or her? Is this person a good role model? Is this person making good decisions? If not, start teaching your daughter how to respond. If she meets a girl and her mother who must imitate and who are afraid to be original thinkers, your daughter can either just ignore the copying and be the best she can be, or maybe she can instill a little confidence in that girl. If that girl says "Why does Tina get the right answers all the time?" then your daughter can say "because I studied and did my homework". If that girl has the same party theme, your daughter can realize that unless it's a wedding with a million dollar designer who is exclusive, party themes don't really matter in the big picture. After all, if you had a party with a theme, you probably used paper products (plates, decorations, party bags, etc) that weren't your original design (e.g., you did a Little Mermaid party and had Ariel hats), or else you held your party at a venue that provided entertainment. Unless you had a private space that no one else has ever had access to, and unless you created a completely unique theme that no one ever has licensed or viewed or even thought of, then it's ok for someone else to throw a similar Little Mermaid party or bowling party or whatever.
Start now to help your daughter figure out what matters and what doesn't. Teach her to smile at the other girl, and to not compete with her, and to not let that girl's imitations bother her. Teach your daughter that if she gets worried about this kind of stuff, later on when she's curing cancer or exploring Mars or raising a baby or writing a book (or all of the above!), it will drive her crazy and she won't get anything accomplished.
Your daughter will take a lot of her lessons from you. If you say "oh, Molly is having the same kind of party you did. Guess that's popular now! I'm glad you had such a fun party and I hope Molly does too" then your daughter won't think this is such a big deal. If Molly's mom buys the same dress, the same shoes, the same everything as your daughter, just say "wow, it's a good thing she has brown hair and you have red hair so you guys won't get mixed up! I hope Molly finds a good style for herself but for now, isn't it nice that she likes your style". Let it roll right off you.
It all starts with you. Relax and enjoy your remarkable daughter.