A heart murmur can mean many different things. I hesitate to tell you my experience because it is not so good, but I do not think that your case will be at all similar. First of all, the doctor probably was not concerned about the heart murmur before this point because he most likely thought it was a regular heart murmur. Many people can have a "heart murmur," which just means that there is a swishing noise that the heart makes during its pumping. This is often a normal functioning noise for some people and does not mean anything about their heart. I have a friend with two daughters who had heart murmurs that turned out to be this kind.
The other kind of heart murmur is one that is a sign of a heart defect. Many times a doctor can tell what defect from the sound and timing of the murmur. I'm assuming that your doc probably assumed that the murmur your daughter has was of the first kind, but because it has not gone away wants it checked for other possibilities. You may very likely go to the specialist appointment to find out that nothing is wrong, so please don't let the rest of this make you worry more than necessary.
First off, let me describe some of the things that they may do at the appointment. My daughter had her first pediatric cardiologist appointment at 2 months old, so it may be a bit different for a 3 1/2 year old, but just in how hard it may be for her to cope with the different situations. You may want to prepare her for what they might do, but tell her that it won't hurt at all. (At least I can think of nothing they would do that would hurt.) We had three tests done while there: a chest x-ray (which for Emma meant she was strapped into a very awkward holder to hold her still, but I don't think they would have to do that for a 3 1/2 year old), a electrocardiogram (I think that was what it was called, but basically consists of putting a whole bunch of wires with sticky pads onto her chest and stomach and using the output from them to tell issues with the heart), and an echocardiogram (which is basically an ultrasound of the heart). Again, all of these were completely painless and my 2 month daughter did very well with them except for the x-ray holder thing.
For us, her heart murmur turned out to be a hold in the wall between her ventricles. Her hole was quite large and required open heart surgery to patch. A hole in the heart (or VSD-ventricular septal defect) is the most common congenital heart defect. Often the hole is not large enough to cause any issues and they can go through life without any correction. If you daughter is not showing signs of struggle with breathing or activity, you may be dealing with something like this. For us, my daughter was having very serious growth and development issues as well as breathing troubles. Despite this the doctors were quite confident that the surgery would go well and correct her problem. In some sense they were correct, it is just that they did not know at that point the other problems she had that showed up after this one issue was corrected. We now think that she was dealing with a genetic chromosome issue. She passed away at 7 months, but they do not think that it was completely due to her heart issues.
Again, I want to say that I do not want you to worry because of our experience. There are most likely other things that would cause a murmur, but I do know that VSD is a common one. But like I also said, it is something that in the absence of other problems can either be ignored, treated with medication, or easily corrected with surgery. If you have more questions for me feel free to ask. I don't mind answering any of your questions. I hope and pray that your daughter is completely fine and that you will come away from the appointment being reassured of that. :)