I don't know how much aspartame gets into the breast milk, but certainly the aspartame isn't good for YOU. A natural sweetener (sugar, stevia, etc.) is much better if you have to have something. Even dark chocolate has some benefit to you. Would a few extra dark chocolate chips satisfy you? I'm not sure if eating the raw cookie dough is a great idea.
If you have such strong cravings, you are missing something in your diet and you might look at an awesome nutritional supplement to give you what you need. It isn't sugar, it's something else probably. Our foods just don't contain the nutrients we need.
I think putting your daughter on whole grains early on is a lot easier than transitioning her from white flour, white pasta, etc. later on. That stuff really works on the blood sugar level and gives people a spike followed by a crash. Whole grains will sustain her longer because they take longer to digest. Remember that whole grain is different from multi-grain. Read the label - if it says "enriched flour" even from various grains (like enriched wheat and enriched rye), then it means they stripped all of the nutrients out and then "enriched" it by putting a little of it back. Go with whole wheat or whole anything else. Start with small quantities and her "system" will handle it fine if you are sure she is getting plenty of fruits and veggies and liquids.
She gets a lot of nutrients from the food that she can get from milk, so I'm not sure what you are worried about her missing.
However, NONE of us gets a full array of nutrients from the food anymore, no matter what it is, so why not consider an excellent nutritional supplement for all of you, which will meet your nutritional needs and help you with your craving, and ensure that both kids get what they need. I'd love to tell you about what worked for my family and the families I work with.