Well my sister had a horse that did that and my mom just changed her bit to a twisted snaffle. So every time her horse pulled put his head done she just gave a little tug at the reins and right away he lifted his head up. So with constant riding and correcting he aventually kept his head at a neutral position.

I have one that when he's frisky he'll haull his head down to try and pull me out of the saddle... I just let go of his mouth and let him fall on his face. Sometimes he buck like that a few times so I have to pop him in the mouth a little to get his head back up. I wouldn't do that unless absolutely neccesarry.
Maybe try riding with a loose rein and make her balance herself. Also does she keep her head down constantly of just throw it down every once in a while? we have a horse at our barn that does this to teach you to ride propperly, but then he does it to be a brat sometimes and we put a standing martingale on him so if he does it he pops himself in the nose.

I agree with Lucinda, don't change her bit yet, especially if she seems to like it. She's not carrying herself, she's leaning on your hands and depending on you to balance her entirely. My horse used to lean on my hands all the time. One way of getting her to stop doing this, is to just drop the reins. If she really is leaning on your hands as much as it seems, she will probably plant her face in the dirt and will think twice about doing it again. Worked for my horse. Trainer said "Just drop him!", I did and he never leaned on me again, he was not a fan of eating arena footing. However saying that, after you get her to stop pulling you down, she needs to learn how to start carrying herself properly. She's not doing it, being lazy and depending on you. Move her forward and get her back-end moving up under her and she will start to carry herself a little more. It will take time, as she probably does not have the strength to do so for a long time right now. Building up her top line, her neck muscles and her back end will all help her start to carry herself properly and stop leaning on your hands.

Look into a new bit, she probably is just really fighting it. Lucinda's answer is great. If a bit doesn't help, I'd look into a chiropractor, as I just talked to one and she said that having their head too low and fighting everything can be a problem in the spine (My horse has a problem with that too).

Another thing to think about is that when you are riding, you are a fulcrum on 2 equal levers like a scale. If the horse is low on the front then you need to stay back more and also get the hind end to engage more to lift up the front. I'd do some backing up exercises to get the horse to engage behind (2 or 3 steps back) and then send her forward with lots of energy.

Also lots of flexing and counter flexing will help her strengthen the correct muscles in her neck.

I would try changing the bit, but also try giving her a looser rein.

Our 4 yo that just went into a program does this, she will also put her little nose in the air to avoid the bit when she wants to run. We started a program yesterday with her and my 16 yo daughter and a reining training. Their first lesson and homework for the next 2 weeks is making Jaz soft. All the tools were taken away...tie downs, side reins, draw reins, harsher bits as they cover the problem and dont fix it. Perfect example is the suggestions of a harsher bit. You go to a harsher bit yet your hands arent soft enough for them, your horses mouth gets harder and the problem arises again so to fix it you go to a harsher bit. Our filly is to remain in the gentle snaffle bit she uses now, and for most of an hour my daughter walked and trotted 10 foot circles asking Jaz to give her face every few feet. As soon as she gave her face the pressure was released. By the end of the lesson you could see a remarkable difference in the filly. Today when they practiced what they learned yesterday you could see such a difference in our filly. And when after "homework" was done and she was allowed to canter the arena she never once put that nose up or too low. I think Clinton Anderson has some videos on how to do this...though after our lesson yesterday we understood it more then we ever did watching a video. As for bits our goal is to put Jaz in a low port shanked bit but NOT because she needs more bit....it wont be until she is soft and has progressed up to a heavier bit...and it will be so more can be asked with less pressure if that makes sense.

If you have a secure seat and soft hands it will soon go away. Ride her and expect her to behave, and when she tries to pull you out of the saddle, brace one hand and let the other rein go slack so that she cannot fight you. Keep her going at the same pace if possible and just gather the rein you let slip and continue on.

By only letting her pull on one rein, you take away 90% of her power. If you do that everytime she will soon stop because she will be thrown off balance every time she tries. Good luck!

Make it uncomfortable for her to lean on the bit.

You can either use a harsher bit (with very light hands, so it mostly only comes into effect when she tries leaning on the bit), or you can let her lean on the bit, and then abandon all contact with the bit (kind like if you're leaning against a door and someone opens it suddenly from the other side).

That's my suggestions :)

My pony used to do this. It is a way for her to avoid work, so when she does this say your at a trot, bring her all the way to a halt with the least amount of strides as possible and then ask her to trot right off again form a halt. This will make her engage her ind end and bring her under herself so she will be using her body rather then you holding her up. Your contact should never be more then just holding her hand. You should not be carrying her. This exercise can work at any gait also. Once you do this a lot, if you can feel her starting to do tho start moving her sideways, almost like a leg yield, or keep your leg on but just pick up your outside hand slightly. Hope this helps:)