That is familiar.
Instead of what age did you suspect your child was gifted, I'll report instances of: "Ummmm, that was really weird."
As an infant strangers stopped, a lot, to engage her and talk to her. I heard a lot of comments about her eyes and much about how alert she was.
At six months obsessed with phone. Always seemed to get a hold of it and seemed to be trying to figure it out. By two she always had someone's phone(real- a toy would not do) and was having imaginary conversations with her "friend", actually pausing at points to laugh and say things like, Oh, I know. If you didn't know better you might have thought someone was actually on the phone.
Nine months would sit and watch an entire Disney movie without stirring and would laugh at the exact same parts every time-This from a colicky baby who spent her first six months screaming bloody murder all the time!
Okay, I'll add this one cause I think it's typical. Used to sneak over to the receiver for the stereo and turn volume all the way up. Then laugh when I turned on the T.V. and almost deafened both of us.
At 10 months she seemed to be communicating with her stuffed animals, hard to explain, you had to be there.
Shortly after and I can't remember(could be up to 14 months) the exact age because I had convinced myself I imagined it, she sight read a word from plain text, no give-away pictures.
Maybe around 15 or 18 months she was counting but not just counting. She was counting backwards and doing other little game like things, clearly playing with them.
More, but dare I bore you.......I will say these events always caused me to have a very "unreal" sensation.
DD6 seemed more "normal", thought she would be the class clown, the "athlete".
At maybe 9 weeks literally spent two days laying on her blanket grunting and turning red and eventually just flipped over from her back to her stomach, or the other way around I can't remember!
I always sang a certain lullaby to her(each girl had their own special one) and she started humming it repetetively at 8 or 9 months.
Started running at 10 months old.
Other than that, she pretty much blended. Except for when she pretended she was a dog for a few weeks at around 2.
We had company from out of town at one point. On old buddy from investment days past and family. She remained in character. That was.....awkward.

DD8 was referred by ped for gifted testing around three. Tested again at age 7.
DD6 was tested right before 5. Test scores were a little lower than sister, but psyd expert opinion, she is the same, bad test day. FWIW- 2nd DD doesn't *look* anything like big sis. Sad to say, I might not have believed it without proof. But that's only because I am an idiot.