That's quite a hardcore route. You'll find Singapore even more advanced than the UK - when I did it in 2003 it was pricier too, I dunno what the status quo is now. Malaysia and Thailand are fine, very well set up for backpackers and travelling on your own will be no issue, there are thousands of backpackers.
As you move on it gets more and more alien. Laos and Vietnam are underdeveloped compared to what you're used to and also compared to the previous countries. Once you get into China (where I was back in November, my 31st country), it becomes harder still. It's exotic, but to the point where there is little familiarity. Even finding a menu outside of global fast food chains that is in English was difficult. The countryside was beautiful, the people very friendly, but almost nobody spoke english - it took the combined efforts of 5 people at Zhangjiajie airport (think Luton) to explain my flight was cancelled for 2 days (yes, days). The climate will vary from tropical in Singapore to Arctic if you take the trans siberian during winter (it runs all year), so that makes it tough to pack everything you'll need. This can be gotten around by buying and dumping kit along the way, but it costs of course.
I found China very rewarding, but the toughest country I've yet visited in terms of ease of travelling around and coping.
On the other hand. The budget you have got is pretty sensible but needs to be trimmed some - Singapore you can knock off in 2 days, Malaysia in a week, Thailand in anything from 2 weeks to 2 months, Laos 2 weeks, Cambodia 2 weeks, Vietnam 2-4 weeks, doing justice to the trans siberian is probably 3 weeks - that's about 13 weeks but that would be non stop and from time to time you'll simply want to stand still and do nothing, recover from a hangover, or just read a book in one place for more than 24 hours. The route and time period are fine, apart from the fact that Mongolia and Russia will be cold possibly, depending on what time you hit them.
The route though isn't the most well travelled for 18 yr olds, they tend to stick to Malaysia/Thailand/Singapore/Bali and then into Australia, NZ, Fiji, Australia, Canada, or a variation of the above. They're also much easier to navigate if this is your first time away from Europe and/or on your own (ie not with family). Just a thought, I don't want to put your fire out, but you need to know how rewarding yet how exhausting this could be.
