I reckon go for it. Having moved to Sydney a year or so ago with DH living in Canberra for work for the first 6 months, I would have absolutely loved if my neighbours had been so welcoming. I'd bake some muffins or something and go over and say, 'I've made a huge batch and we won't finish them all so I thought you might like them'. Take her cues, if she invites you in then go, but if she seems like it is a really bad time then just leave it at that.

You never know, she migh be a BB'er and already know you are coming (lol)

Spring xx