Lots of good advice here. I can't imagine how anyone could cope with two babies under one, tbh (although I know that lots of people do - parents of twins for example). I think a good way to judge whether someone else can do something is to think how you would cope yourself in the situation where two babies were crying.
Imo, it would be better to find someone with older children - whether their own or not - at least at first. Later on, when both babies are over 2 and your neighbour has gained some experience of childminding, you could move your DD, and as she already knows the neighbour, that wouldn't be as difficult for her as moving sometimes can be.
Have you thought of putting her in a nursery, btw? I did that with my youngest child and two of my grandchildren are in nurseries. I prefer them to child minders when the children are small because I think that looking after babies is such hard work it's better if the carers have the support of other adults - who would also ensure that they were caring properly for the children - and the established rules, routines, facilities etc of a nursery.
I have also put children with child minders in the past, and they have been, without exception, fantastic, warm, loving people and the children were very happy there - so no criticism at all of child minders. In fact I feel disloyal to the lovely people who have looked after my children over the years by writing that I prefer nurseries. And I agree that child minders often do put other people's children first. It's just that, imo, having more adults around is a better bet when they are babies, if you are unsure.
I think the problem you might have if you decide not to ask your neighbour, is how to tell her without causing offence. I would go with something along the lines of 'I'd like DD to be with older children so it's more like a normal family group/she could learn from them' or 'I'd like DD to be nearer my work than my home so I could get to her quickly if she was ill etc'.
You could show her you trust her by asking her to babysit (on a reciprocal basis) or sharing childcare at weekends, asking her advice, etc.
Good luck. 