How soon is too soon is different for everyone, there's no right or wrong to it. The longest I have ever been without a pet of some sort was around 6 months and that was due to being a lodger somewhere rather than having my own place (and even then I bonded quite well with the landlady's poodle, so I wasn't without animal company).
Giving a home to another is not a betrayal, it is a wonderful act of generosity when you are still grieving - and if your children wanted her then it's all good. You can grieve and come to love the new arrival at the same time