There has been talk that the Queen might not open Parliament in person if it looks like MPs won’t vote for the Speech From the Throne. According to an article on Politics Home by Paul Waugh, Her Majesty might give the State Opening of Parliament a miss if her Government might fall.
If the Queen doesn’t show up, there will still be a Speech From the Throne since, by convention, peers and MPs cannot transact business until they have heard the Sovereign’s reasons for summoning Parliament. However, the speech would be delivered by Lords Commissioners, just like at prorogation. Having Lords Commissioners deliver the Speech From the Throne was often standard operating procedure during Victoria’s reign when she was cloistered away mourning Prince Albert, but the current Queen has been assiduous about opening Parliament in person. She has only missed the ceremony on two occasions (1959 and 1963), and in both cases it was due to pregnancy rather than any constitutional controversy.
The Telegraph‘s Philip Johnston seems annoyed that the Lord Chancellor wouldn’t be the one to read the Queen’s Speech for her (although several Lords Commissioners take part in the ceremony, only one actually reads the speech!). He attributes this to Labour’s “constitutional vandalism,” which is a bit silly. It’s true that, before Labour tinkered with the office of Lord Chancellor, he was usually the one who read the speech. But now that the Lord Chancellor is an MP rather than a peer, the Leader of the House of Lords has taken over his role as principal Lord Commissioner. However, this isn’t cast in stone. Indeed, the Lord Chancellor is still formally a Commissioner just like the Archbishop of Canterbury, and there’s no reason why he couldn’t read the Queen’s Speech. There are precedents for a Lord Chancellor who isn’t a peer presiding as principal Lord Commissioner. When John Bercow was first confirmed as Speaker of the House of Commons in 2009, Jack Straw signified the Queen’s approbation even though he was an MP. Similarly, Frederick Elwyn Jones and Sir Michael Havers both presided over the Opening of Parliament (in 1974 and 1987, respectively) even though they were neither peers nor MPs.
I would be a bit surprised if the Queen bowed out of the State Opening. When Stanley Baldwin pressed ahead with a Speech From the Throne after losing his majority in the December 1923 election, George V read the speech in the usual manner. A precarious Government would likely encourage Her Majesty to attend since a her absence absence would only highlight their weakness. Thanks to the unnamed royal sources who are blabbing to the media, Ministers couldn’t even use the Queen’s age as a fig leaf. If Her Majesty doesn’t show up, people will assume that it’s because she has doubts about the Government’s viability, and that’s an awkward position for a constitutional monarch to be in.
UPDATE: the Times reports that the Queen will deliver the Speech From the Throne no matter what. Apparently, Whitehall wasn’t keen on the idea of her skipping the speech, and it was feared that such an act could politicize the Crown.
 The Sovereign hasn’t prorogued Parliament in person since 1854.
 Ultimately, the Queen decides who should preside. Although the Lords’ Standing Order 76 states that, when Parliament is to be prorogued in the Queen’s absence, the Commission shall be “directed unto some of the Lords of the Upper House,” this does not bind Her Majesty. See House of Lords Procedure Committee, Second Report: Royal Commissions for Prorogation (HL 135), para. 6.
 Jack Straw wanted to take part in prorogation as well, and he asked the House of Lords to change their Standing Orders to replace the reference to “Lords of the Upper House” with “Lords of Her Majesty’s Privy Council.” See the aforementioned report of the Procedure Committee on Commissions for Prorogation.
 This refers to the formalities at the very beginning of a Parliament and is not the same as the State Opening of Parliament.
 However, both men received peerages shortly thereafter.