If you really believe this is the only job offer you will ever get for the rest of your life, then you should accept the extension, hope it turns into a full-time position, and put those silly travel dreams out of your mind.
If you think this company, and perhaps other companies, will still want you and your skills after a year, then travel and enjoy.
What I have discovered in my work life is that every job I "lost" opened up an opportunity to an even better option. Talk to your current company and tell them what you want to do - there's no point in keeping it a secret. Tell them you have been working and studying flat-out your entire life, and want and need a break. Let's see how they respond.
And please try not to worry about your age. Starting your career at 23, 24, or 25 - it really doesn't matter. To a 40-year old, they all look the same! No one's going to question you about it.