That is a tough one. Those types of records, listing all the births or deaths in a particular family, were obviously created after the fact. I looked for a few pages before and after and saw no dual dating nor notations of "O.S.", etc. In the absence of any indication to the contrary, I'd assume the Quakers used the style of the day, thus Old Style up to 1752 and New Style afterwards.
I guess it's also possible you could find additional records for some of the people--gravestones, etc. that could also help. But really, it's only a matter of a few months one way or the other.