Does she need to have a party at all this year? If there's a possibility you might be in labour, or about to start, I wouldn't even worry about a party. She's too young to realise anyway, and if your family/friends don't agree with it well *raspberries* to them and you can have one next year or during warmer weather instead?
DD is almost in the middle of July, we haven't had a party for her yet, but I have no idea what we'll do when she does get a party. Is hiring a gazebo for the backyard or a smallish function room an option?