TJ – you are being contrary as usual.
'Normal' implies a certain regionality. 'Normal' is what happens 'round here' and 'round here' isn't a flat country that has a largely cycle-sensitive or specific infrastructure. Culture plays a part in all of this as well as the physiical limitations of the human body.
OP – get a bike trailer and, if you REALLY MUST drag the bairn around at such an early age, put them in their car seat secured into the trailer. Given they won't remember a damn thing, I hope your personal urges are sated by this activity. Personally, I've been waiting and TT Jr had her first trailer ride secured this way at 6 months.