The sexing will take about 8 to 12 weeks. There are many traits you can look at. this site is full of answers to the same question. Try searching for how to sex a turkey or something similar.
13 weeks is a long time to wait to geet your birds out of the brooder and on to the ground. 6 weeks is quoted fairly often, and 8 weeks comes up a lot. As I just commented on another post, hens let their poults run around on the ground almost immediately. So who knows, really. I'm sure people have tried putting them out at different ages and had different experiences. I put all mine from the brooder to the turkey fortress at 6 weeks. I have never had any disease related mortality once in the pasture. I have had one case of wry neck and a couple cases of temporary sluggishness, but not immediately. Most birds are absolutely fine.
I'm sure someone will say I am way to careless with my poults (people already have), but its worked for me, and its cold up here when i put them out. They huddle together at night to keep warm sometimes, but they make it.