On a bit of a vacation so this will be brief. I'm going to leave out any sort of deal talk involving some of the other pitchers because I didn't get a chance to grab all of them. Thanks to Alan Fawcett, Alex Howard, Robert Schiff, Wally, Chaos, Chaz R, and John Doerr for the E Jax questions, which I've combined a bit here.
Outside of a FA acquisition or trade, who would fill the void? Lannan? Garcia? Duke? Who's in the minors?
Lannan is the obvious candidate. He's a pitcher the Nats (or at least Rizzo) don't particularly like, who makes a lot of money (relatively), who will be a free agent after next year, but who is young enough that his value as a back of the rotation guy should be stable enough to attract attention. Therefore you pitch him, don't really hurt yourself (because he is a decent #5) and you try to deal him.
Outside of Lannan pickings get slim fast. Everyone likes what they saw of Garcia but the 64 innings he pitched this year were his most since 2005. He needs to be stretched out and it'll take a year at least. On the older side the Nats had Zack Duke look ok in AAA this year. Once a Pirate staple, now a baseball vagabond, he's likely to take a job that gives him a better shot at a major league rotation. I'd expect to see Yunesky Maya, if only because Rizzo hates to admit a mistake, although he did have a decent AAA season. As for younger pitchers, you might see a Jeff Mandel or a Trevor Holder depending on how their 2013s go, but neither are considered good prospects.
What is then promising for the future that we might see next year? Two names, Daniel Rosenbaum and Alex Meyer. Rosenbaum is more likely to be seen first, having already pitched well in AA. He's improved consistently in the minors, has excellent command, and is a ground ball type of guy. He's not young per se but just young enough. Meyer is the true prospect, live arm type of guy who has been progressing ok for a year now, but he's only hit high-A so far so I really doubt you'd see him before September.
Should they give him a qualifying offer?
Yes. Edwin is good enough that you wouldn't mind having him back next year at fair market value and you don't want to lose a potential draft pick you would get by making the offer. There isn't a terrible downside here unless you think the Nats REALLY want to jettison EJax.
Without Edwin Jackson would the rotation worse than what he started last year with?
Well maybe technically, but it wouldn't be worse than what Rizzo thought he had when he opened 2012. Strasburg is guaranteed the whole year. ZNN was great. Gio blossomed into a Cy Young contender. Detwiler looks better than Edwin. In hindsight yes, losing Jackson will potentially make it worse, but the Nats will be opening with much higher expectations from the rotation with or without him