The thing is, lots of people will say 'well I didn't encourage any gender stereotyping but my boy loves x'. Problem is, you cannot be that objective.
There have been studies of people holding a newborn baby and the language used to describe the baby is noted. When the baby is dressed as a girl it is 'fragile, delicate, sweet, pretty, tiny'. The exact same baby in a blue outfit was described as 'strong, determined, handsome' etc. From the very beginning, our reactions to the sex of our child have an influence on who they are.
You say that your husband never changes the toilet roll so I suspect you do. The changing of the toilet roll in your house is done by a woman. Your dd has done it once and it's been commented on. She'll do it again now because it got her some attention. The joke that it's a woman thing is already happening. The precedent has been set.
I see the 'boys are like Labradors' thing on here a lot (maybe even said already, I've had to stop typing three times to answer the door). Boys are painted as 'simple creatures' who need only food and exercise. This does a massive disservice to our boys and to the men they will be. It's horribly patronising too. We all need food and exercise, it's just championed in boys and then we wonder why women aren't encouraged into sport. You will similarly see girls described as complicated or bitchy, setting them against each other from the beginning, comparing them unfavourably to their uncomplicated male counterparts.
You can't answer the nature/nurture thing really with any degree of confidence. The way we talk about children and the way we treat them is so influenced by our own socialisation.
I think you can say, generally, that small children are not so different from each other. They have the same needs and the same potential. Things like hormones will make a difference of course but you cannot control the socialisation of humans from the moment they're born and sadly, that seems to decide who we are in a lot of arenas.