Hi Katie,
Absolutely. The kind of diapers definitely make a difference. Her age actually shouldn't make a difference as to whether or not she gets a rash. There are so many chemicals in disposable diapers that even though they are super absorbant, its the chemicals that make the diapers work that irritate skin. The chemicals and lack of air in there, pull all the moisture (even natural skin moisture) away from your child.
7th Generation is definitely a much better alternative to the other brands. And no, they are not going to hold up like the others, but you are doing your daughter a favor as well as the earth.
I don't know the specific health benefits for girls (I have boys), but I do seem to remember that those chemicals in "other" store bought diaps were linked to infertility in boys. Something about all the chemicals and the high temperature that wreak havoc on the testicles. My guess is that one probably wouldn't want to use something on girls that might cause infertility in boys.
If you google "health issues when using disposable diapers" or something along those lines, there are some very interesting (and scary) statistics. I am sure that I wrote more than you needed (or wanted) to know. We use cloth, so I am used to having to do LOTS of diaper changes a day.
Congrats on making a better choice for your daughter.
B.