Firstly, I'd hug them and tell them that I love them just as they are. Then I'd ask them the name they'd prefer to be called, and if they have a specific set of pronouns they'd prefer - THEN I'd use that name, and those pronouns, and tell them to go wash up, it's time for dinner.
(and continue to use that name, and those pronouns forever more, as well as supporting them in their transition if that was what was desired by them - not all transgender people desire to transition)
Why? Because, they are still my child. I did not care if they were male or female when I carried them, I just wanted them to be healthy and happy. Why should that change just because they are no longer in utero?
I have a child, who are the moment is too young to pronounce their own name clearly (SOOOO close), but if they were to come to me with this type of revelation, I would do exactly what I've laid out above.
Age? I'd believe them, and support them whatever the age - sure as a very small child I wouldn't rush out and get them into endocrinologists etc - as I am aware small children often which they could do things that other children (who happened to be the other gender) do etc - but if it continued etc, then I would look into those who can help with supporting and transitioning (delaying puberty etc...).
I mean, Cis-gendered (physical and non-physical gender match) people KNOW they are which ever gender they are from birth, and most people who identify as transgender express that they knew from a VERY young age that they were in the wrong gendered body.
I don't think it would be any different if it was my daughter who advised she was my son, or vice versa either.