I took my daughter to a shopping center when she was about 4 or so weeks old. I kept her in the pram unless for feeds and didn't let people touch her or hold her mainly because strangers. I was also out and about with her via bus though as I don't drive and had to take her up to the doctors or appts via bus. This was 2.5 years ago. I now have a 11 day old baby and I've taken him out to appts and to places because we have things going on with the toddler xx
2 weeks old we went out becuase we had to no choice and was actually nice just to be strolling
Supermarket when its quieter may be a good way to ease you in, they also have lots of choice for clothes
Can you order online? I don’t think there’s anything wrong with going with her now personally but in terms of your rest and stress levels online shopping might just be easier?