Hi there,
My DS, Daniel started the short naps around that age as well. It also tended to impact on his night sleep which was rotten as you have to deal with a grumpy baby during the day when you are tired yourself. He is 18 weeks now and, in the last week, has really started to pull together both his night sleep and his naps so it does get better and there is hope. For once, he has read the books which say he ought to get it at around four months (though I expect he will go back to his old ways at least occasionally).
Here's what has worked for me. When he was around your DD's age, I would run in and give him the dummy when he woke and started fussing. It took 2 or 3 goes but he would then normally sleep for about 2 hours total. That stopped working after a while so I had to sit with him for about half an hour holding the dummy in, hand on chest, and stroking head (if I could do all that with two hands). Then he would sometimes go back down and sleep for another 45 minutes. That stopped working when he just got too interactive and was distracted by me being there (and he went off the dummy). For a while I did nothing and lived with the 45 minute naps and then as he got older started to extend his awake time and see if he would resettle himself after he woke. This has been working and he has gradually got quicker and quicker to resettle and today didn't wake at all for any of his naps. But there are still days when he doesn't resettle and he has to be got up tired.
When he did get up and was still tired, I sometimes just let him sit on my knee quietly or lie down on my bed with him so that he didn't get too grumpy. Or in the afternoons when he was really cross I would take him out in the buggy as he would be quiet then and, eventually, fall asleep. Also, if you want to avoid a build up of overtiredness, then I found that when DS was about your DD's age, he would do more than 45 minutes in the buggy or the sling because the motion helped him through the wake up jolt (no chance of that now as he is just too interested in everything that's going on). So, although you do need to keep your DD napping in her cot, then it can give you a bit of a break and end the cycle of overtiredness.
Time is the key, I'm afraid. I've also found that as DS gets older then he is more easily distracted from being tired if he hasn't napped well. When he was younger he would just cry and go into meltdown by the afternoon whereas now he just gets a bit grumpy so he is easier to live with.
Good luck with it all. Hoping your short napping phase is very short.
Freddie