Kel-Tec PMR-30 in .22WMR, 30-round capacity semi-auto pistol.
A couple random thoughts:
1) .22WMR is loud, yea it's a lot smaller than a lot of other rounds out there, but it's loud and in a different way than 9mm, .357, .45 ACP, etc. If you're in a self-defense situation and are firing a .22WMR, you're likely going to discharge a series of four, five, or more of them, which could result in some hearing loss, moreso than two rounds of 9 - .45. Peak amplitude isn't what typically causes hearing damange, it is an integration, i.e., overall impulse (area under the curve) over time.
2) Rimfire cartridges have a significantly higher failure rate compared to centerfire, it's inherent in the method of initiation. I would not personally trust a rimfire round to save my life for this reason alone. There are also concerns about reliable feeding of a long, skinny cartridge like the .22WMR in a semiauto.
3) Depending on your location and how people dress, 40gr .22WMR rounds may have difficultly penetrating clothing and skin with sufficient energy to damage structures of the central nervous system, assuming they are on-target. Hence, the .22WMR round will not reliably incapacitate an attacker as will a round that penetrates deeper and delivers greater energy.
4) One more.. you can't dry-fire a rimfire pistol like you can a centerfire pistol. Dry-fire is one of the most important types of practice, especially for somebody who can't shoot a lot of rounds at the range too frequently.
Hope it helps. I agree with Glenn, a .38 special (+P if she can work up to it, at least for "carry" ammo) with wadcutters out of a 3" barrel on a metal frame may be the ticket.