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Welcome!
There is no one perfect telescope even for a 4 yo. I could recommend a handful of different 'scopes as will others. Do you or your husband have an interest in the stars too?
I think for your budget you could get a short 80/400 (f5) refractor on an AZ3 mount. (About $250). It will show you the Moon and low power sweeps of the stars. It will show you the planets but you need a 3x Barlow in your kit and use it with an eyepiece between 9 and 12mm. The 15mm Superview eyepiece is wonderful for this telescope. One thing you will learn though is that this telescope shows chromatic aberration on planets (any short achromatic refractor does). Another option is a 70/700 (f10) refractor but also on an AZ3 mount if you can get it as the mount usually offered is not very good.
Either of the above telescopes you can keep for a lifetime (especially 80/400) but it won't be your last telescope. If her interest grows then perhaps at the age of 11-13 you could get a 6" f 8 Dobsonian or an 8" f6 Dobsonian.
Note the 80/400 refractor can easily be used for nature study during the day as often they come with a 45 deg correct image diagonal. This refractor is known as a short SW80, ST80 short tube; the main characteristic being 80mm diameter objective lens and 400mm focal length. It usually comes with a 25mm and 10mm eyepiece which are Ok but a 15mm wide angle is really nice in it. These all give low power views with the 10mm giving 40x (400/10). This is nice for the Moon. Add a 2x or 3x Barlow and you have 80x and 120x. The telescope will not take any more power very well. Note do not get a 5x Barlow sas it enhances the chromatic aberration as the power is too high for such a short achromatic refractor.
Also NEVER let her observe anything near the field of the Sun as it will blind in an instant without proper filtration on the main 'scope and finder.
Note the above 'scopes are not toys but you can certainly get toy telescopes as cheap as $99. They will show you the Moon.
Whatever you choose, enjoy!
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