Did you get frost? If you did, there's a chance that the tree won't make it. Even if you haven't gotten frost, you'll want to bring the tree inside just to be safe. Since it was grown from seed, you probably don't know the variety and what "Hardiness Zone" it will survive in.USDA Plant Hardiness Zone Map
The question on how long it will take to bear fruit is kinda tricky. If it survives, don't count on getting fruit for at least 4 years. It could be as many as 8 years before it is ready to bear fruit. Even if it gets to the blooming/bearing stage, you don't know if your tree is self pollinating or not: i.e you may need pollen from another peach tree to get it to bear fruit. You also need to know that the resulting fruit is not going to be the same as the one that your daughter ate. Propagation via seed (sexual reproduction) will produce genetically diverse offspring. It could be bigger or smaller, sweeter or more bland, better or worse than the original.
Good luck with your peach tree. Let us know how it goes.