Personally, I would stay at the current job for 1 year. However, I would let my boss know what I have been offered a new job but not taking it (depending on how close he is with his boss, may not be a good idea). World is too small. At some point, you always end up meeting same people again if you are living in the same city.
Career Advice: If new work is more interesting and have better options, go for it. But before quit current work, let your boss know that you have family obligations and need more money and got a bette offer. If he can match the same or better, he would like to stay. After all, its business. I am sure his boss negotiated with him too when he joined this company.
Brutally Honest: It all depends on job satisfaction. If he is satisfied at current job, even it is little less, stick with it because you do not know about new job.