My son is also allergic to dairy and we put alot of veggies in front of him with dips like hummus and ranch. He won't eat some things at first but the more you introduce a food, the more likely they will eat it. It can take up to 10-15 tries so don't give up. We give our kids lots of fresh veggies and fruits for snack.
Like celery, carrots, red, orange and yellow peppers etc. Any fruit is good too. And remember that the fruit tastes sweeter if not served with or after a sugary treat:-)

Some Simple suggestions:

Sometimes children dislike strong flavors- I find it surprising that she likes broccoli. Often small children don't like the mess or texture of sauces or cassroles or find beans too mushy, making it more tricky. I hated beans of all kinds and now love them, so there is hope.

Try:

Spaghetti squash with some vegan butter and s&p.

Oven baked sweet potato fries made with olive oil spray and rolled in chili powder or thyme (non spicy or Italian) and salt.

Imagine brand pureed veggies soups- carrot and sweet corn might be a big hit with some cornbread.

Fajitas (peppers, tomatoes, onions)- the fun of assembling her own taco with lettuce, faux sour cream, etc. may distract her from the veggies involved.

Zucchini bread

Gardenburgers

She probably would love some more creamy things since she can't have dairy- some fake dairy can go a long way. Mild-garlic hummus for dipping?

Follow Your Heart makes the absolute best dairy-free cheese (no casein either if her allergy is really severe). It melts and everything. Try Tofutti sour cream and cream chesse. Good luck! Don't give up and have lots of variety!

I have found a children's nutrition book which could be very helpful. Children seem to really enjoy this book. There is a website that tells about the book with some examples. The website is www.tommythetomato.com

Wow! Allot of good advice on this topic. My twins did not become "picky eaters" until they hit preschool, when they heard other children make coments to the teacher at lunch "I don't like this or that" This is where my battle begun.
Kids love to "be involved" so I came up with the idea of a garden. I let the kids pick out the vegetables we would plant, looking at the pictures on the seed package. They each got to choose two. This was enough to tend to until "mom" knew what she was doing too. They planted, watered, helped weed, and harvest the vegetable. Since "they" grew it they were more inclined to "eat" it. I raved on how good "their" carrots were, or the radishes. This started 3 years ago when they were 3, and our garden had trippled in size. Fresh organic vegetables and money saver now I am learning how to preserve the fruits of our labor.