CaptainMal said:
I say go for it. Teach her to shoot and have fun. Most cases she won't get a shot anyhow. It will still be fun for both of you.
I agree with teaching her how to shoot, but I cannot agree with "Just go for it" in any way. If you (CaptainMal) are aware that the caliber is not sufficient, going for it is irresponsible. Deer are living animals that will suffer from a botched shot with too small a round. And if she does get a shot and either loses the deer, or it runs off to suffer and bleed out for a few hours until you track it, it will likely ruin her desire to hunt and at least ruin the day.
Get her a proper rifle that will sufficiently kill the animal quickly and humanely. That way if she does get a shot, it's something she can enjoy. The last thing you want is for her to have a horrible day chasing a wounded animal when she is just starting.
If she can kill the deer quickly by herself, she will have much more fun than if she just injures it. That way she will want to go again.
Here are 3 affordable rifles that are plenty capable of taking deer. The 30/30 can be loaded a little light and still be plenty effective. The .44 Mag will easily take deer to 100yds, maybe even a bit farther with a stout handload tailored for use in a rifle. You can easily reduce the recoil in a Handi Rifle by adding a good thick Pachmayer Decelerator recoil pad, or other pad of quality, and even add a mercury recoil reducer in the stock bolt hole behind the butt pad.
Mercury recoil reducers
http://www.brownells.com/.aspx/cid=0/k=mercury+recoil+reducer/t=P/ksubmit=y/Products/All/search=mercury_recoil_reducer
.243 Handi Rifle w/3-9x40 scope
http://www.nefguns.com/item/64848_HR_Rifles_Shotguns_HR_SBS-243_Handi-Rifle_S.aspx
30/30 Handi Rifle
http://www.nefguns.com/item/6826_HR_Rifles_Shotguns_HR_SB2-231_Handi-Rifle_S.aspx
.44 Mag Handi Rifle
http://www.nefguns.com/item/78835_HR_Rifles_Shotguns_NEF_HANDI-RIFLE_44MAG_BL_.aspx