Travel finances can vary greatly. In North America and South America (my trip so far) I've been told it is absolutely impossible to travel for less than $100 per day, yet I have proof that it can be done with $45 USD per day (including absolutely everything, such as shipping the bike from Panama to Colombia), and I am confident that if I really wanted I could have done it for half that cost. Just depends on how you are willing to travel. Keep in mind, however, that if you sacrifice too much you might not enjoy the trip and will burn out early. This is why I do not choose to travel cheaper than I do. I hear Africa is cheaper than the Americas. There are also ways to earn money on the road. Play an instrument on the street (busking). Fix things for people. Work at a farm. Work at a bar. Work at a hostel. Search this site for other ideas.
There is absolutely no reason a 125cc bike is unsuitable for the trip. I am currently on the road with a 650cc bike (KLR 650) and frequently would prefer a 250cc. 33bhp is not enough? The KLR only has 37bhp and as I just noted, I would be happy with less. Starting the trip again right now, I would probably choose something around the range of 250cc - 450cc.
Don't worry about a lack of experience on the bike. Be careful and you will get that experience VERY fast. You will be practicing every day. But find someone to teach you a bit about off-road riding. Even if you don't intend to leave pavement, you will appreciate having the skill because paved roads in many countries look a lot more like dirt roads in places like the USA. But I highly recommend you do find dirt roads and remote locations as they are frequently the best parts of the trip. Also consider this: The smaller the bike, the more places you can go. On a KLR650 I regularly go places that a bigger/heaver BMW GS or KTM would not consider, but there are still many times I REALLY wish I had chosen a smaller bike.
If you think a lack of travel experience is a problem, read books such as "Jupiter's Travels" or "One Man Caravan". Common sense and patience go a long way. I may be older than you, but before leaving on this trip I'd never traveled more than two weeks at a time, never out of the country, and only once on a motorcycle. I never considered my lack of experience a problem.
Same for repairs. Lots of people traveling have no knowledge about repairs at all. But if you want to learn to repair a bike, something small will be far easier to work on. I carry a clymer manual for my bike so that I can look at it while doing repairs. I do not need it very often any more, and will probably throw it away if that trend continues.
Good luck on your travels. If this is something you want to do, I guarantee there is a way to make it happen.
Traveling The World Since:
Bike: KLR 650