I would make a list of things you and your daughter like.
Instead of planting right away, I'd do some planning.
A 4x4 foot space is small. You still need to do some preparation.
If this is not a raised planter but in the the ground, then you will have to do some digging and amending. the following is a link to the basics of building a small garden using the square foot garden plan.
https://thefoodproject.org/sites/default ... 2012_2.pdf
I would start a few seeds in small pots first while to get them started and plant them out. It will save time and space later. Don't plant a whole packet only a few seeds at a time and plant them out when they are ready. and start new seeds every few weeks for succession. This works for plants that mature early like lettuce and spinach. The following link is to a site with good information on how to grow using a square foot garden method
If you and your kid likes or can acquire the taste Swiss chard, kale, and herbs will give you repeat harvests from only a few plants. One each of kale and Swiss chard will produce over a long time and they don't get really bad problems. Green onions and chives are easy plants that are cut and come again.
While I like tomatoes, cucumbers, pole beans, peppers, and peas they need more than water. A trellis would be needed or some other support. They get mildew so it is not a good choice when it rains a lot so they are best planted in the warmer months.
You will need to fertilize and check the plants for insects and disease and take care of those things promptly. No matter when you plant you will need to learn how to determine how often you need to water. And there is always a bit of weeding to be done.
If you had more space I would have these plants on the list NZ hot weather spinach, cherry tomatoes, kale, swiss chard, sweet potato, fennel, dwf french marigolds, green onions and chives. The NZ hot weather spinach,tomatoes, and sweet potatoes need space to sprawl but you can't eat NZ spinach fast enough once it is established, Sweet potato leaves are also edible. Fennel and marigolds just have to be somewhere in the yard not in the vegetable garden. They will help with attracting beneficial insects and Florence fennel produces an edible bulb when it is still young and it tastes like licorice. Cherry tomatoes are the most productive they can sprawl or be supported on a trellis, but they do better in warmer weather.
Until you get the hang of it just grow one or two different kinds of plants and add more as your skill level increases. The garden will look bare in the beginning but plants will fill out the space and need room to grow. I would use the square foot grid and a ruler in the beginning to make sure you get the spacing right.
Gardening can be rewarding but even in a small space it takes more than just watering. However, it would be a good learning project for you and your daughter and you can share the chores.