Your best bet is to buy an accessory flash
I am going to guess that you are using either lens zoomed almost completely out to take the pictures, so your effective f-stop will be the lower of the two numbers (i.e. 5.6 and 4.5). Than being the case you will be better off using the 40-150 because it is going to give you more light. Even using that lens you are probably not going to be able to get a shutter speed of 1/500th at an ASA of 1600. I have shot in a lot of gyms and can't recall ever shooting in one that bright. Also, 1/500th may not be fast enough to stop all of the action.
Your money would be better spent on a good flash that mounts on the hot shoe attachment on the top of your camera. A better flash will put out significantly more light and completely avoid the low power internal flash. It will give you the added bonus of not continually draining the main battery.
A flash will trigger at a much higher rate than your shutter speed will ever be able to match, so set your ASA somewhere that will give you good quality and let the flash stop the action. You may get a dark background with heavy shadows, but I am guessing that you are more interested in seeing your daughter than what is behind her.
One last suggestion, if you decide to work with a high ASA, high shutter speed and low aperture setting try to time the photos so that the subject is at the top of the jump. There is an instant when the subject actually stops moving up, and starts to go down that will result in much sharper pictures.
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