S.H.
Make sure, that in the mornings... she gets lots of runaround time... physical stuff.
Kids this age, need that.
Then, have lunch, keeping things low key, calm etc.
Plan things so that lunch and after is not a 'rushing' around type thing.
After lunch, have her wind-down... keep things quiet/calm/turn things off.
Then verbally cue her, "nap time soon...." then do your pre-nap routine.....
SAME routine, everyday.
It cues them.
My son is now 4 and naps everyday. If he does not, like your child, he turns into a TROLL and does not last all day without a nap. He still sleeps fine at night, by 8:30pm for bed. His naps are 2 hours, at least. He naps well.
Since she is now 3... they need runaround time. Getting their physicality out.
all the best,
Susan