DSLRs are big, yes, bigger than compacts at any rate, but certainly not clumsy. If size is going to be an issue, it's definitely a contributing factor in whether you should go for one or not. However, I would recommend taking a visit to your nearest camera retailer, be it Currys, Jessops, John Lewis, wherever, so long as it's somewhere that will allow you to demo a camera. Have a play with one or more of the DSLRs there. You'll be surprised at how light and compact many of the entry level models can be.
As for getting yourself the best value for money, it's a delicate balance. Whilst the actual image quality between different models won't very hugely, what each model allows you to do with the camera can. I'd probably recommend avoiding the lowest tier entry models like the Canon 1100D or Nikon D3000, look at the Canon 550/600D or Nikon D5100 for bodies that will be less restrictive in terms of features. There probably won't be much need for you to go looking at the upper mid-range of things, like the 60D or D7000, however, as you're moving straight on from a compact, and may well decide after your travels that you don't want to continue shooting with a DSLR, so getting a higher range body might be wasteful. Don't feel like buying a lower end body is a poor investment if you do stick with it, however. I'll get back to this later.
The more important place to spend your money for better quality images is on the glass, your lenses. Think about what you'll want to shoot whilst you're away. Landscapes will demand a nice wide angle lens, whilst other tourist attractions and interesting sights may not allow you to get right up close, so a telephoto lens will be in order. Maybe you'll want to be taking lots of photos at night, or in other low light situations. The best way to deal with this and keep image quality high, and minimise high ISO noise (that grainy look you get when shooting in low light on a compact), is to use a wide aperture prime lens. These are just the basics of what you might want.
Here's just an example set up for you consisting of a 550D camera body and three different lenses, one tele zoom, one wide angle zoom, and one standard fast prime, all for around £1000.
http://www.amazon.co.uk/Canon-Digital-C ... 72K33TPHJKhttp://www.amazon.co.uk/Canon-EF-50-1-8 ... 800&sr=1-1http://www.amazon.co.uk/Canon-EF-S-55-2 ... 800&sr=1-3http://www.amazon.co.uk/Canon-EF-S-17-8 ... 156&sr=1-1I know £1000 sounds like a lot, but consider this, those lenses will work on any future Canon body you might upgrade to. Unlike compact cameras, you're investing in a system that will last you for years and years. This was what I meant about not splurging all your money on a top end body, as if you really like shooting DSLR when you get back, and decide you want to do it bigger and better, the old body can be sold and replaced with an upgraded model. The real investment is in lenses. On the other hand, the lenses are just that, lenses. They're glass and various mechanisms, so they won't become outdated, and as such, will maintain a moderate value on the second hand market. This can also be used to your advantage when buying all your kit in the first place. You could probably save a fair bit buying second hand bodies and lenses. If you're not fussed about video features, an older model from Canon or Nikon without video capabilities can be had much cheaper second hand than their current versions that do include a feature you may not want or need.
This is all just generally speaking, if you have any more specifics you'd like covered, feel free to ask.