She doesn't just say "breastfeeding prevents pregnancy", if you click the external link you'll see that she elaborates and specifies that there's a bit involved in ensuring it's effective.
Kellymom is a fabulous resource, I wouldn't discredit all of her evidence because you know people who've gotten pregnant while breastfeeding (and yes of course it happens, but even things like occasional pumping or skipped feeds can interfere with its effectiveness as BC).
And yes, you can find studies that suggest weaning before six months is okay; some even claim it's beneficial. However, until those are recognized and accepted by health organizations (the WHO in particular), they don't hold much merit.
Health organizations are responsible for sifting through all of these conflicting studies and deciding which have the most convincing results. These people, I am sure, are much more equip to make those calls than those of us sitting on Google.
There is certainly something to be said for a doctor's input since they know your child as an individual. But, it's been pretty widely accepted for a while now that putting any solids in a bottle is a choking hazard, so based on that advice alone, I'd seek a second opinion.
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