Typical modern roses with bolt-upright growth are normally pruned fairly heavily in order to control their height and encourage new shoots from the base. Typical pruning height might be 18-24 inches. Cut above a growth bud. If the center pith is brown, cut down until you find clean pith. (Tan pith is OK on old barky canes, white pith for young green canes.)

First, Fireweed, don't be afraid of doing the wrong thing. QE is a hoss of a rose that is strong enough to forgive us all of our pruning errors. And believe me, I've made plenty. I have had the same QE for 20 years now, and she survived all my missteps to become the queen of the rose bed.
Your instincts are good. Wimpy or dead canes need to be removed. After that, do a little haircutting for shape. Keep the inside open for air circulation. Try also to eliminate crossing canes, which will rub against one another to the detriment of both. Courage is required--this is not easy to do if both are strong new growth.
Know that Queen Elizabeth is stately. Seven feet is not unusual. Resist the urge to prune her down to 4-5 feet. Her royal highness will not be happy. If I remember rightly, this rose is the reason why the category "grandiflora" was invented--and if I'm wrong, Jeri or Kim or one of the real experts on the forum will set me straight.

Kay

my neighbors wanted to prune their QE and the rest but they were going to prune like hack them down I was worried so I got some cuttings from them just in case they did... luckly they didn't (they are getting old so I will just ask them if I could in the fall just to be sure :)....) She is getting tall and when I got the cuttings I tended to her a little but gesh those thorns are huge....

Here is my neighbors QE

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Wow, JessicaBe. That is what my QE used to look like. I had to move her 6 years ago and she's just not as happy as before. Time to get out the Alfalfa pellets and give her a treat.

Once you've taken out the dead wood and spindly or crossing canes you can prune as much or as little as you want for height. If you'd like the plant to be shorter cut it deep now. If you'd like it tall like your neighbor's leave the length on it. QE will grow no matter how you prune it, lol!

So it is alright to prune now Seil since you live in the state above me?

Yes, QE can grow about a foot per month of growing season, say 6-7 feet above pruning height. Because modern bush roses tend to flower at the top of the plant, I prefer to keep the top within reaching distance. When I kept QE, it didn't mind being pruned down to 24". But it's the grower's choice.

Now is the perfect time to hard prune. In normal weather conditions the roses would be just waking up and you would be just starting your spring prune. It's only because of this weird early spring that things have leafed out so early. But there is still plenty of time to prune back your roses.

I was mistaken!! To all (and sundry) who have given so much advice on pruning what I thought was a QE, I apologize! I DO have a glorious hybrid pink rose which did reach 8' this year! But! I realize now I don't know Who she is. I've looked at mine vs QE and there are too many differences. Some while ago, I began filling in a check list from the American Rose Society to see if it was a known rose but I've never gotten around to completing it. I've added a few photos to share with Pink Rose fans! I just don't have any recent ones showing her height this year and I've pruned back a bit after the first blooms faded

1 more pic of Ms. Pink

I was going through the roses and the one that was something else was the electron rose---such a deep pink. They said it was a hybrid could that one be yours by chance??

Here is one of my Lizzy rose last year when in flower and I am happy to say she survived the winter as I covered all of mine with burlap. Really missed seeing them over the winter--so happy to see all the ones I planted last year pulled through with flying colors-the knockout in red, the coral drift rose, the lizzie rose and the always and forever tea rose and the double pink knockout. :) And she has a big bud on her this year and yet another smaller one.

I found a shot of 'Mz Pink' at 7' that I took in June to right of miniature peachy yellow rose, behind Kaiserin Auguste Victoria, with La France to the right behind a miniature white not yet in flower.