William was microchipped at about 8 or 9 months old and his has gradually migrated down his left shoulder and into his left armpit. It's been there for a couple of years now so I think it's stopped moving at last.
Louis was microchipped at about 3 or 4 months and as far as I know his has stayed in the right place.
Whatever you decide, the advice given about getting Betsy used to visiting the vet and thinking it's a nice experience is good advice. Take her in to be weighed, fussed by the receptionists or nurses, anything really that helps her to feel calm and confident there.
Another thing that's really useful is getting her used to being examined and touched all over right from day one. Spend a few seconds a couple of times a day gently lifting her ears and looking into them, touching and lifting her paws one by one, feeling her all over, including her head, tail and tummy with gentle praise and rewards. You can also get her used to having her teeth looked at by gently opening her mouth just a little at first, then a bit more, saying something like "teeth" when she opens her mouth so that it becomes a command that she understands.