It really sounds like you are well on the right path to helping your daughter get a little more activity into her day (walking together, planning activities for the Summer, etc). Since you have said she enjoys walking on the treadmill - and walking in general- I think your plan to purchase one is fantastic. Also, you sound like you have a wonderful view on trying to help your daughter implement a healthy lifestyle without damaging her view of herself.
Some of the suggestions previous posters have given are great, but I can understand that with other children to consider and limited resources it can be difficult to find something low-cost to do as a family while still remaining active or even find time to take up one-on-one activities with her.
Since she is expressing an interest to become more active, I definately think it would be beneficial to help her begin some kind of activity while her motivation is high. Have you asked her what kinds of activities she would like to do?
Maybe you can pick up a booklet from your local YMCA/community recreation center and go through the choices together to help her pick out something she would enjoy doing. Even though this isn't an activity you would do together, it would help her gain great skills in other areas that relate to team work, being part of a team, and interracting with peers (and give you some free time while she is at the YMCA who doesn't love that? Or more time to spend with the other kids). It's a good idea, although this could be too expensive for you to consider as an option... Explore other opportunities your community offers. Some YMCAs have family time sessions, or you can play pool, go swimming, or use the gymnasium together (usually free or $1 per child/low cost).
What about yoga as a family? There are some great books or resources available online with kid-friendly positions to try (even my young dc enjoys doing a 20 minute yoga session with me). This would be a no-cost option that you can all do at home or in the yard. The Healthy Kids website (
www.healthykids.com) has a few good poses to begin with, they can be found at:
http://www.healthykids.com/hk/slides...1&catref=HK139
Is there another family you can buddy up with to get outdoors together? Going to the park to throw the frisbee, non-competitive FUN games of soccer or basketball (family vs family or children vs adults), or nature hikes are some ways of adding a little more interest instead of limiting activities to being only within your family.
Can she keep an exercise journal? You said she liked to read, does she also enjoy writing? She could enter how much exercise she did (even small amounts of 10 minutes at a time are beneficial, and you indicated that she really doesn't need to lose a lot of weight, but that you prefer she be a little more active), how she felt about the activity, how her body felt afterwards, the changes she has seen in herself (physical, emotional, assertiveness, confidence etc) and she can see how far she has come.
Playing tennis together sounds like a fun way to get your heart rates up without being too strenuous. Great idea!
Can you draw a hopscotch grid on the sidewalk with some chalk for family fun? Playing tag, hide-and-seek, jumping rope all burn calories and can be done as a family. If time allows for it when you're out and about, take the stairs or park the car further away from the entrance (or walk, like you already do).
Some gymnastics academies offer a "free play" session where the kids get to try and play with different gymnastics equipment. Are there local places that offer an all ages session like this (usually a few hours each week)? Or buy your own mini-trampoline as a pp suggested...
What about setting up a scavanger hunt around the block, or even at the mall/in the house? Simon Says? Are your other children old enough to organise a game of Capture the flag or something similar? A family sports carnival day where you set up games of beanbag races, baton races, or other types of relay races you can enjoy as a family (or compete with another family/extended family). Even bowling counts. What matters most is that you're doing something active as a family!
Your library should have some books on ideas to keep your family fit (even for those who don't enjoy sports). What kinds of books does your daughter read? Is there a way that you could incorporate her favourite characters/interests into a creative physical activity or game?
Honestly, it sounds like you already have some good ideas to start introducing a more active lifestyle into your lives as a family! Well done! Maybe after a few weeks of hiking, you could have a "marathon" together?
As for the food, you mentioned that while your daughter eats healthy (for the most part), she perhaps tends to overeat/choose large portions. You could try giving her smaller portions or switching to a large variety of healthier foods (more vegetable portions, low-calorie recipes, etc). You could even have her help prepare simple dishes (making salads, easy recipes, etc - if you don't already).
I think it's great that you're making better choices for your daughter while she is still young enough to keep them as a lasting part of her life!
**Edited to add that I understood the op's post to be more about ways to get her daughter to be more active, not about dieting/restricting calories for her dd. I am sure she understands how damaging that might be to her dd, both physically and emotionally. I think introducing physical activity into your family life is fantastic, and the benefits are a healthy way to burn energy, be fit and have fun as a family even if weight loss isn't an incentive.