6 week old in public?

My mums Christmas gift to me was after I had baby we would go out shopping to get some new clothes!

My question is can I take my baby into town / city centre without having his jabs yet? I am breastfeeding and craving some me time even if I can just get a new bra that actually fits!!!

I feel abit uncomfortable about it but my OH said he will be fine because my milk contains antibodies? What do you think??? Shall I wait or go for it???