If this is a chronic problem, I believe the advice is: if she is crying when she wakes up, try to settle her in the bed with pat/shh, if not able-->take her out and start routine again from winddown so this won't become a habit. If she awakes and seems happy to play and you think 45 minute naps are enough for her, then play until time to feed (EASA essentially). I'd visit the 45 minute posts at the top of the naps page. If this is just a once in a while (or even once a day) thing, then you can choose to do either activity (like last post says with shorter A time after eating) or sleep routine again based on what you think she needs. Don't let fear get in the way of using W2S if it is a chronic problem or it will not get better for a while. I've heard it may get better around 6 months. My DD is 12 weeks too and that sure seems far away.
Wish you luck!