The age difference is not really that big. The issue seems to be whether you sense that she is ready for a committed relationship, or still wants to explore her options. From what you've briefly shared, you notice a sort of a change when she gets back from visiting her friends.
You may be right, that she is using your vasectomy as an excuse. If the relationship had moved fast, is a long distance relationship and she already has a child, all of these are factors that will impact her behavior.
If you are giving her space, make sure she understand that it is to allow her to think, instead of her interpreting it that you are distancing yourself. Be careful because this statement of hers that she's confused and wants to figure things out, does not have to involve the two of you to "give her space" It may be her way of distancing herself as to where the two of you eventually move your own ways. Her statement that she is "confused" needs spaces etc, may be a way of sabotaging the relationship (for whatever reason)
You may want to ask yourself 1/ what does she really want out of a relationship 2/ is she ready for a committed relationship, 3/ what is she willing and capable of bringing to the relationship (She had said she'd move near you) 4/ if she does not relocate, realistically what is the future of this relationship 5/ what do you want