You'll be very hard pressed to find trouble in
Turkey imho of course. On top of that, Antalya is a very foreigner friendly city.
We're in
Turkey with our 1.5 yo daughter and the only thing I can't get used to is that Turkish really like
kids and they always pay attention to her (no, not in a creepy way - I'd have felt it).
Maybe think twice about going somewhere close to the border with Syria, otherwise I really don't think you have anything special to worry about.