When vaccines are given too early, they are totally ineffective. Current recommendations would say that 6 weeks is much too young to begin vaccinating toy breeds. Even though 3 rounds have been given (which is the current recommendation), the first round probably didn't do much, and perhaps the 2nd round as well.
I am very cautious when it comes to vaccinating, but in this case I would most likely give one more round (but not for another 3 weeks) followed by the booster. But, I would not give rabies until at least 6 months. If your furbaby has already has the intranasal bordatella, I would not give it again until 6 months has passed.
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