What dippymother said.
Both my dd's have been bored for a short while when they came to the end of their time in a particular group or nursery, which used to manifest itself in the whole "don't like nursery, don't want to go" routine. And resolved as soon as they were moved into a new group/setting.
But I don't think it's about being bored academically tbh, just feeling that they've 'done' that group and need something new. That could be a new room, new children, new teacher, new activities, whatever.
My dd2 is 4 and in a school nursery class which is fantastically creative and lateral with the kids, but not particularly academically orientated (although they do very light letter and number work). Dd2 can in fact read fairly fluently, and comes to me every morning wanting to 'do letters books'. But I'd be horrified if the school were doing extra reading with her -- i'd rather they were doing extra glueing, cooking, acting, music, dance and school trips. If your dd is bored, then it's not a sign that the nursery is not sufficently academically advanced for her, rather that they're not making enough effort to come up with activities that are new and interesting for her and make her feel like a big grown-up girl.
Before dd2 started at her school nursery she was in an even more mad, arty, bohemian setting, where they positively boycotted the literacy and numeracy end of things in favour of cooking, making their own scented playdough, huge baths of waterplay with shaving foam and roaming dinosaurs, fruit tastings, colouring tubs of basmati rice, making little figures out of mis-shapen vegetables, making popcorn and throwing parties with soundtracks ranging from reggae to thrash metal. I defy any child to be bored with that lot on offer.
There's a whole world of stuff 3 and 4 yearolds should be doing at nursery. They're going to spend the rest of their lives reading, but only a short time to paddle in chopped-up green jelly or cook spaghetti, dye it pink and chuck it around the room.
That's the kind of thing you should encourage the nursery to do, not extra reading and writing!