we moved from our old house that had the lead problem, so not so applicable nowadays.
I think that's about correct, it can't penetrate the fur, and the mineral load in the water is already so high when you have "hard" water, that not much lead can be absorbed into it -- unless it's hot water. Hot water, especially in soft water areas, can absorb a lot of lead (old housing in Glasgow at especially high risk). You can send a water sample off to the county laboratory, btw, pay them a small fee, tell them why you are concerned, and they will write a report for you about how serious a problem (or not) they think the lead levels are in your drinking water supply. Contact your County Council.
Looking back I sometimes wish we had just moved house. But I had conflicting advice and I suppose in the end we did a sort of middle ground set of measures between the different bits of advice.
Can you get the pipes replaced in your house? DH is practical that he did this himself, in our old house, within a month of us moving in (before we realised what a lead problem there might be in the woodwork and carpets).
You can also get your baby a blood test to see what the lead levels are in their blood. This may put your mind at rest. But I warn you that watching them draw blood from your baby is horrendous (DS was also 10 months old when he had his blood taken). Then my GP was very dismissive about the results, which would be considered elevated in the USA (and borderline unhealthy in the UK). GP said something to the effect that all children in our area were probably about the same, it was just an environmental effect, so not to worry (so hey, it's ok if my child is being poisoned as long as it happens to everyone else in the neighbourhood, too, is it??).
So something to watch out for, health professionals may be totally unsupportive if you want to look into this.