The key with fiber/constipation is the amount of water you drink. This was part of the problem with Freya when she struggled as we switched to solids. You can eat fiber until it's coming out of your ears, but if you're not drinking enough, it just sits there in your gut. Ow.
There are however, foods that are likely to cause constipation in children (though not always), such as bananas or applesauce.
Also, it's important to note that whole grains are generally recommended to be introduced later than fruits/veg. No longer is it recommended that babies avoid them, just that they take it slow, as some whole grains (particularly wheat) can be hard for immature tummies to digest.
Kassandra, we used flax oil with much success too; I was relieved after having a couple of turns with suppositories before that. There are lots of food items that can help with constipation too, they just work to varying degrees. Peaches still show up on the menu here, even at a year, if we're having trouble. Dr. Sears has a good page about natural rememdies:
http://www.askdrsears.com/topics/childhood-illnesses/constipation. I know this thread's about baby food, but just wanted to put in two pence, since F struggled for awhile too.
On the fruit purees, she should be able to have anything except citrus at this age, but if she's only had purees so far, be sure to strain peaches, etc. very well. You might try giving her small bites of cut banana to try as well.