I've recently witnessed a friend going through this (we became friends after his partner had died) and tbh I think it's very complex. He was seeing someone else seven months after his dp had died, and they were living together within months. But, while I think that in their way they are happy, I think that there are a lot of issues wrt his grief which he has not really dealt with, and that to a large extent his getting involved with someone else (who is also a friend) he has moved on in order to escape his grief.
In itself that isn't necessarily a bad thing (there are no children involved so it's only himself to think of), but in reality that grief has come out in different ways, e.g. he suddenly couldn't bear to live in the house any more so they moved - within weeks - even though the house isn't sold yet, into a rented flat halfway around the country, although on the positive that is nearer to his family. His dp on the other hand has had to move into the house of someone who, by virtue of the fact she is dead, has essentially been sainted. Even though she essentially was very controlling and kept my friend isolated from all his friends and family (none of them saw him for the six years they were together). But because she is dead this can never be pointed out, but the fact he is now seeing his friends and family has IMO shown him that it wasn't all fantastic and that too has been a difficult revellation.
I also think that not all women who end up with someone who is bereaved are doormats or being used - I think there are a lot of manipulative women who go after the bereaved, I saw this first hand in the number of women who went after my friend with the idea that they would be the one to "get him over his grief,"
and there were also the ones who fancied the idea of his big house which he inherited (it was his dp's house). 
I think that no relationship comes with a guarantee, and that ultimately we all have to do what makes us happy. I do also think there isn't a set time, as what works for one doesn't work for someone else and vice versa.
Also, why is it wrong to say, enter into a new relationship within a matter of months, but nobody would criticise someone for conceiving a baby months after losing a child? We wouldn't consider having another baby to be replacing a dead child, so why are we fit to judge someone who moves into a new relationship?