I like Susan's suggestions of open-ended conversations. Here are some other things that come to mind:
What to do when whining (especially unproductive whining) starts? I just wrote up a blog post on this. Much of this depends on our response. One technique I use, when appropriate, is to write down the "I wants" on a big list. I don't counter with reasons why the child can't have it or my opinions on their choices, I just sit and take dictation. Sometimes, kids just need to have a place to put the "I want" thought down and with some children, this helps them move on. They feel listened to, and all you need to say is "Let me think about this for a while..." and you take it from there. This might mean picking one thing off the list every couple of weeks. Or it might look like parsing down the list to come up with a couple options that work and choosing one to start. "The List" and "Let Me Think" buy us some time so that we know what we adults want to do before re-entering the conversation.
When the whining starts/persists after I've been clear with my "no, not now", a little check-in may be in order. I often ask: "Do you think that if you keep asking me about this, I will change my mind?" Many children have answered a convinced "YES!" to this question. Now comes the reality-check. "I've been pretty clear with my answer. (Repeat your answer once more. ie-- "we will have ice cream tomorrow" or "we are staying until the end of the ninth inning") and I'm all done talking about this with you. You may talk about it, but I'm done." And then actively ignore the child. That is to say, you are keeping an ear out for her conversation to change to something more agreeable, and when she is able to move past the whining, you do too. Start up a more pleasant, distracting conversation and if it reverts back to whining, just restate the "I'm finished talking about this" only once. I like this method because it gives the child limits without forcing them not to talk about it...You stay consistent, and over continued consistent use, the child will learn that Mom means what she says the first time. It also gives a social context for whining and complaining... no one really likes to give a lot of attention to whiners and complainers.
The ultimate goal of the above techniques (I call them my "pat answers") is to give the undesired behavior very little attention. Often, our kids get us into endless 'reasoning' with them, which often doesn't hold much value other than our Getting Sucked In, until both parties are engaged and miserable. Disengaging gives us more authority and gives them clear boundaries that we aren't going to do *That Dance* with them. One can only argue with no one for so long, and the same goes for whining with no audience. I have had tantrums occasionally emerge in a few instances, however, it's my belief that the children in question were kind of on their way to a tantrum long before our interaction. (Tired or emotionally exhausted and this just seemed to be the last straw.) In the case you were describing, where your daughter's needs had been met, having boundaries around how much you are going to be nagged is appropriate.
You had mentioned gratitude, and I was also wondering if your daughter has opportunities to make positive contributions around the house. Sometimes, this can help to change the perspective a little from MeMeMe to Us. At her age, she can help fold towels, some of her own clothes, make "deliveries" of laundry to their appropriate rooms or drawers. She can help with washing/putting away silverware and setting/clearing the table. She can help feed and care for a pet. She can do some light housework with you, so that if you are say, scrubbing the toilet in the bathroom, she can use a sponge and soap to give the sink a wash, or wipe down the side of the tub or cupboards. She can be a helper at the store, bagging up produce as you shop, counting out how many cans of food you need, carrying boxes to the cart and then help unpack at home. You aren't going for mastery here, but for participation, so it mightn't be perfect, but she gets to feel good about helping with some 'grown up' stuff. And don't link toys or allowance to this at her age-- it's very fuzzy thinking, that. It's morally good for youngsters to experience themselves as helpful.
I hope that you can find an idea or two here that will work for you. I'll be keeping my eyes open to see what other insights other moms have. Best wishes-- this is a tough age!