The little round carrots like Paris Market Atlas are easier to grow in pots than normal carrots that need a lot of space and depth to develop.
Self supporting dwarf peas and beans are best for pots and you don't need canes (a bit of a safety hazard with a toddler). Varieties like Tom Thumb, Kelvedon Wonder (peas) and Hestia (beans).
You can also get micro tomato plants, some which will grow in a 9cm pot (Micro Tom) but there a lots of small bush varieties. I would chose a blight resistant variety. Dwarf courgettes (Eight Ball), aubergines (Ophelia) and cauliflowers (Igloo) are good in pots too. Dix Huit radishes are ready to crop in only 18 days.
Cut and come again salad leaves are always useful. Lambs lettuce is also good to grow in pots. If you have any peas left without room to grow them, you can cram them into a pot to eat as pea shoots.
You can also get compact/dwarf/trailing varieties of redcurrants, blackberries, raspberries and blueberries, to go with your strawberries.
If you buy potted herbs in the supermarket, you can divide them up into multiple pots.
Don't forget to sow your seeds in succession (ie one pot of peas, then another pot 2 weeks later) so you get multiple crops.