THere are two different sorts of quarantines.
One is to determine whether an animal that bit you was likely to have been able to give YOU rabies. An animal w/rabies infection only contagious for a week or so before it dies (contagiousness beings approx the same time as symptoms do). Thus, if the animal remains healthy-lookin' for ten days, it is pretty much 100% guaranteed that it did not have the CONTAGIOUS stage of rabies when it bit you.
However, it can take months and months before a rabies-infected animal starts to show symptoms and become contagious. Six months is a sort of reasonable ball-park figure that many jurisdictions use for holding animals to determine whetyer they may be INFECTED WITH rabies but just not showin' it yet. (Really paranoid jurisdictions, such as island nations that are rabies-free, sometimes require a 1 *year* quarantine to prove the animal isn't carrying rabies!).
The second of these things is what the o.p.'s vet was talking about. And indeed, because contagiousness can sometimes precede symptoms by a day or so, and because earlly rabies symptoms can easily be missed (chalked up to some more common problem), it seems to me like a sensible attitude when there are young children in the house. (Children are more vulnerable to rabies, for various reasons but small body size plays a considerable part in it).
Hope you can find someone to take it for you for the 6 months, good luck!,
Pat