The word for “someone of the same age” in Russian is ровесник when applied to a man and ровесница when applied to a woman. We have a similar word in English, coeval, but I don't think I've ever heard anyone use it out loud. If the question «Кто из вас старше?» “Which one of you is older?” is directed to a couple of men of the same age, they may respond «Мы ровесники», and if the question is directed to a couple of women, they may respond «Мы ровесницы». If the question is directed to a groups of mixed gender, then the masculine form is used, «Мы ровесники». (By the way, that's generally true in most Indo-european languages. The masculine form of a word often has two roles: the gender-specific masculine meaning, and a generic meaning that can be used for mixed groups.) There is another pair of words, masculine сверстник and feminine сверстница, which mean the same thing and can be used the same way, however they are not quite as common as ровесник/ровесница; they are still pretty common, though.

Of course, if those were the only ways to express the idea, Russian wouldn't be very interesting. Here are some alternatives:

The «Мы одного возраста» phrase is perfectly good written and spoken Russian. The phrase with masculine однолеток or feminine однолетка is conversational; I don't recommend writing it. The same holds true for the phrase with masculine одногодок or feminine одногодка.

The phrase with «по» may be the most natural sounding in response to «Сколько вам лет» “How old are you?”, but you wouldn't expect it in response to «Кто из вас старше?»