With Pfeiffer (our girl), we waited until she was around 7-8mths or so bc her teeth still needed to finish. Also, she was small like your girl. You do run the chance of her going into heat, but we waited and our vet very much supported it even at the risk of a possible heat. Our vet felt the chance of a heat was very slim. As for the chip, I'd wait...it's something that isn't absolutely crucial at this time, so if it were me I'd wait until she was under.
