you must go to Grizedale Forest which has some really easy flat walks with sculptures and musical instruments on the way. It also has a really good adventure playground & cafe.
Also Brockholes on Windermere is good with walks, picnic areas & very good playground.
And Fell foot park simialrly - boat rides, playground, cafe, lots of space to run around.
Your DD would love the steamer accross Windermere and propably the Steam train from Haverthwaite.
For walking you copuld try Gummers How - ds is 4 in June and has walked it. If you go the more gentle way round & you get a fab viwe over Windermemre. Make sure you get an ordonnance survey map.
Another nice easy walk is Tarn Hows - round small lake, not hilly and then you can stop at the Drunken Duck for a pint - they have lovely beer garden too.
The Swan pub at Newby Bridge (bottom of Windermere) does good food, has a marina & a good play area in the garden
The Aquarium of the Lakes is good for a rainy day and a bit further afiend the animal park at Dalton is very good for a day out.
Yes it is suitable for 4 yr old!