The carseat is a tough call. If she is a confident sitter then you probably won't need it. If she isn't sitting well then going to restaurants etc is more difficult without the carrier since she can't use the high chair. IMHO, you will use it such a short time, can you borrow one? (make sure manufactured date is less than 5 years ago
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As far as the swing goes, I would definitely check out the manual that came with it. Some give an age limit (under 6 months for ours) and other models give a weight limit (25 lbs. for example) or even an activity level limit (can't put an active child in it - i.e. one who may climb out
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Good luck!