some ideas for you, things you could look at:
You could take some examples of reinforcement of traditional gender roles in ads aimed at children: both directly related to the product being advertised, like girls playing with Barbies, dolls, clothes, makeup, cooking, and boys playing construction, cars, action figures. But it's also interesting to look at the deeper layer of the ads. Say you have an ad for children, you should also look at who else is depicted in the ad, for example they will usually be shown at home with their mother in a traditional stay at home role. So it would be interesting if you analyse the gender roles which are hinted at by the toys, but the other, more subtle roles hinted at in the background (like mum being at home looking after them). and also break it down into what is depicted visually, but also the type of language used, 'princesses' for girls and 'little monsters' for boys, the way boys and girls are talked about in the ads, tone of voice, lighting etc.
Then you can also look at ads not aimed at children but which children see because it's during their viewing time, for example for detergents or whatever, again, always showing 'mum' doing the household tasks and having the main responsibility for the house. all this influences children's ideas about the world.
You could also think about the aims of the advertiser, they don't (usually) want to make people feel in any way uncomfortable, or to challenge their beliefs except when it makes them keener on the brand or product. So their motivations will lead to them reinforcing more conservative stereotypes.
You can also explore the child's world, for them the boundaries between advertising and actual TV programmes are not that clear. it is all just stories and information which are shaping their world, allied with what they see at home. So their sister at home could love train sets, but girls on screen are all girly and love sparkly nail polish or whatever, and that will influence their ideas about what girls are like.
You could also explore the question of who drives these gender ideas, are the advertisers just reflecting society, or are the parents asking for these sexist products, or are children asking for them. and what about the manufacturers, making toys for increasingly global markets, it might be easier to produce stereotyped toys than not. you could take each category of user like that and break down their possible needs and motivations.
another interesting one is the blue versus pink phenomenon, fairly recent, where the parent and child consumers are more or less forced to select either a blue or a pink variant of a toy, e.g. the fairly recent phenomenon of toys intended for both genders (like easels or pogo sticks) being produced in such a way that there is a pink girls' one and a blue boys' one and nothing in between and the impact of that.
good luck!