Ratbastid makes a good point - if you are very up-front with the new girl and she is game .. take things at a pace that you are comfortable with.
My last relationship (best thing that ever happened to me) started while I was still recovering from a long-term relationship. I was very honest and up front about how I felt and it brought me even closer to the girl I was seeing (my most recent ex).
Be prepared to feel awkward as hell - but use that 'gut check' to keep your pace comfortable for you. If the new girl is really interested in you - she will let you know if your pace is too fast or too slow
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Summary: tell the new girl and go for it