Any gift that is connected to the lunar horoscope animal is always great! Since the baby will be born in the year of the rat, look for cute toys or accessories featuring mice or hamsters. There isn't a big distinction between "rat" and "mice". Rat sounds less pleasant so most Chinese people call the baby a "little mouse". People also look for amusing connections between the animal and the human, so rat year babies like tiny cosy spaces, hiding food etc. My DD was born in the year of the dog and she often carries toys around in her mouth like a puppy.
Anything with the colour red is also perfect for gifts. Especially in connection with the lunar horoscope, there's a superstition that you should wear something red during your birth year. This is typically a red belt, bracelet or underwear (lol). For babies, their first year is obviously their birth year as well so something red and cute won't go amiss. Off the top of my head these would be very good gifts:
- A tiny red baby hat, with round (hamster-like) ears if possible
- A red swaddling blanket or towel. This is totally random but the hospital I gave birth in (not in China) wrapped all their babies in dark red bath towels. This made sense as they get a similar sensation of being inside the womb and they're most familiar with dark red.
- Toys, rattles, dummies with mouse designs on them. Babies can't really appreciate toys until they're 3 months old so I found practical gifts like clothing or blankets more useful in the newborn days.
Cash is also a traditional gift but usually reserved for family members and also more strongly associated with weddings and lunar new year. I wouldn't have expected money from my friends as a baby gift, and it might even feel slightly awkward.
The "month sitting" tradition is very flexible. I stayed home for a month but I was more than happy to have visitors and show them the baby soon after birth. I was very grateful for food though!
Rice & chicken congee is another healing recipe that is very popular after childbirth or illness. It's basically jasmine/sushi rice simmered in chicken broth for a very long time so it's got a porridge consistency. Also contains shredded chicken, ginger and coriander.
Fruit is a surprisingly popular gift in China. People would take crates of apples or oranges along when visiting. If you don't have time to make food to bring along, then a basket of healthy and easy-to-eat fruits like bananas, apples, mandarins would definitely be appreciated. I would also have loved filling snacks like nut bars, cereal bars, cookies etc.
Wishing your friend all the best with her baby!