First, three very important tips:
Take extra batteries and memory cards, that $2000+ you can't afford lens is of no use if you battery is empty.
Try to rent equipment if possible, buying a good general purpose lens is ok but if you want to get a super-telephoto wildlife lens you will only use once - rent it.
Make sure you are familiar with your new equipment and can use it reasonably quickly with good results before you leave home.
Are you going to be taking pictures while hiking/driving/touring or are you going to go to places specifically for taking pictures and have the time to set up (swap lenses, setup tripod, etc.)?
If you are going to be taking pictures while touring you want general purpose equipment so you don't have to stop and delay everyone while you set up (also, you don't want the animals to run away before you photograph them) - a consumer super-zoom like the 18-135 or the 18-200 is the best choice in terms of cost, weight and size, the image quality will be similar to your 18-55.
A step up will be the 70-200 f/4L non-IS (the reason I recommend the non-IS version is the price) or maybe a 70-300, it's cheap compared to the quality you get and it's still a good general purpose lens (especially if you also take the 18-55 for cases you want the wider angle)
For animals in the wild, especially smaller animals, 200mm won't really do it - I don't have any lenses longer than 200mm so I don't know from personal experience what focal length you do need.
Update about the review you posted -
He used a full frame camera, so a 70-200 on your camera is like a 112-320 for him, likewise a 70-300 is like a 112-480 (so, a 70-300 will cover just under 80% of his shots)
Add your 18-55 for wide angle landscape (that's like 28-88 for him, a focal length range he almost didn't use - but you can shoot panoramas to simulate a wider lens) and you are set.
You can get a super-wide angle lens (the canon 10-22 or the sigma 8-16), but in the review almost half the pictures were taken at the max focal length so it seems wiser to invest in the long end if you have extra money. (the 100-400 he recommends, for example)