Well, I'm not keen on the idea that there is one set of activities which are suitable for girls and a different set of activities which are suitable for boys.
I try to give my daughters the idea that they can be engineers, scientists, astronauts or dragon-tamers (ok, maybe lion-tamers) if they want to be when they grow up, and not limit their options to female-stereotype careers such as beautician or manicurist. So I try to give them opportunities to play in ways that in the 1950's would have been considered 'boyish' - and then it's up to them what they actually choose (and it's ok with me whether they choose to play with trains or play with dolls) .
- Kids should decide for themselves what they think is fun. Why put these limits on play?
- Play matters. Children need a wide range of play to develop different skills. ...
- The real world has moved on. These gender stereotypes are tired and out of date.
Let Toys Be Toys - For Girls And Boys: Why It Matters
So the obvious answer is to say that you should do with her whatever things you did with your son at that age. But I realise that's not necessarily a helpful answer! So - some suggestions:
Activities related to things she's interested in
With one of our daughters that was ballet and drama, with our other daughter it was steam trains and racing cars. Either way is good.Activities relating to things that you're interested in.
It's really fun sharing an adult interest with a small child - if you have an enthusiasm then it can really rub off on them.Dinosaurs. Everybody loves dinosaurs. :)
So once you've got some kind of a subject or topic, the actual activities that you do (based on that topic) could be almost anything:
Junk modelling (this is particularly fun if you do it really big)
Painting and drawing
Role-play type playing ("you be a racing car and I'll be the other racing car!")
Playing with 'small world' toys (ones that represent objects in the adult world e.g. toy cars or dolls)
Building with construction toys such as Lego
Playing running-around games ("you're the T Rex and we're the stegosauruses and you have to catch us and then we'll swap around!")
Making up stories together
Reading stories relating to the subject together
Reading non-fiction children's books about the subject together
Going to an event or show e.g. a sports fixture or a ballet performance
Board games and similar e.g. Dino-opoly, Top Trumps (they have TT for practically everything now), etc etc
Going to a relevant museum e.g. for cars we've been to Brooklands, for ballet/performance we've been to the Theatre and Performance gallery of the V&A.
Watching relevant movies or TV shows together (not too much)
Of course there's other things that everyone does with kids that aren't themed but are equally suitable for either gender: going to the playground, playing on the climbing frame, climbing a tree, playing chess, feeding the ducks, playing snakes and ladders.
It depends on the individual child and their preferences. What does she like doing?