Palm trees don't need trimming, so any fronds you remove are simply to improve the aesthetics.
I like to cut away all the older, tattered palms just prior to spring for one simple reason — once warmer weather hits, the new growth will start pouring out from the top of the tree, and your palm will look fantastic and healthy despite their recent haircut.
I like to cut out all of the older fronds all the way up to the newest, freshest growth from last year. It sounds severe, but palm trees are basically a type of grass, so it is really hard to hurt it unless you cut off the growing top, center-most shoots (don't do that).
For the old, woody fronds encircling the lower trunk, if you leave them, they will eventually fall off on their own. I tend to give them a good pull each year to see which are pretty much ready to come loose (I prefer the look of the bare trunk underneath), but they will come off easily in their own good time. If you want to cut them off sooner, it will not hurt the tree. Overall, Queen Palms pretty much take care of themselves.