If you intend to actively support City throughout your kid's childhood and inlcude her in it by taking her to games whenever possible, then you're doing the right thing.
But if you intend to just pack it all in and only follow them on the TV, then I can see the argument for letting her follow a team closer to home so that she can experience it for real (although that's probably not as easy as it sounds due to you living on the island).
For example, if I lived in London and couldn't be arsed to go up to Manchester for the occasional match, it'd be wrong to force City onto my kid cos he'd miss out on everything it means to be a proper fan just cos his dad was a lazy shit!! Would be much better for him to follow one of the local cockney sides and he could go with his mates then.