For specific bikes, I can't comment, but I can say you are well within the realms of a "normal" bike. Yes, neither of you are tall, but you aren't needing a bike with special adaptations for short riders (look at Islabikes if you do).
I am going to add to the chorus of people suggesting a bike recycling project's bikes. Six reasons:
- You get a receipt, so you know it is not stolen.
- It is more likely to be sorted than any off-the-peg bike from a big chain store, serviced and ready for work. You can't say that about new bikes from a chain store.
- Cheaper, obvs.
- Better for the environment
- Less attractive to thieves.
I think you'd be very well served by an older (late 80s/early 90s) non-suspension mountain bike with slick tyres. In many ways, these are the perfect bike for general transport with heavy loads (a child counts as a heavy load). They are not too sophisticated so easy to work on, they have decent brakes (in practice, for the type of use you're describing all modern bikAes have decent brakes) and they are strong, with compact, rather overbuilt frames which keep the centre of gravity down and are very rigid for attaching racks and child seats. Great for luggage carrying, which is why many people use them for round-the-world touring. That also makes them perfect for carrying children!
There might also be cycle training too, which is something to consider.
This is an example of a decent bike for your situation (albeit you'd want a smaller one). Something that looks like this is ideal. Ignore any labels of a "ladies" frame - engineering wise, there is no such thing as a ladies frame. Low step designs like this are practical for bikes where you don't want to swing your leg over the top.
Anything else? Yes. Mudguards will keep you and the kid dry and free of mud, and a lock will mean you get to keep the bike longer. If you have a new, shiny bike it is much more likely to be pinched, so you need a more expensive lock - another thing in favour of these older machines.
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