How about a blow-up paddling pool and a big bag of those plastic balls. I know - it's plastic, but there's no batteries! And the pool can double up as a paddling pool. We talk our daughter to the soft play centre for her 1st birthday yesterday - it was her first visit and she had a great time playing in the ball pit.
Personally, I have a list in my mind of things I'd like her to have between now and Christmas, and I'm going to buy her anything she isn't given at our family gathering on Saturday... She's an only, so there'll be no older siblings to tell she's being hard-done-by 
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My list includes a ball pool, a wooden trike, a jack-in-the-box, wooden puzzles, lift-the-flap books, a little rocking 'horse' (I know that she's been given a rocking dinosaur!) and a little garden slide. She already has a wooden toddle truck with blocks in. A few relatives have already 'bagsied' some items, so they don't get duplicated, so I know that all bar the jack-in-the-box, puzzles and books are definitely on their way. She is a very lucky girl. TBH, if she gets everything I feel she needs, I'm not going to buy anything else - I'll save my money until I can find something good, rather than just buying something now for the sake of it. I did buy a bookcase for the nursery at Easter though, and with such generous relatives she's certainly not going to go short. Besides, she is too young to really know who bought her what at the moment.
Does that list help?