I've very recently found a new job in in England from Japan. Realistically, a time frame just isn't possible. This entirely depends on your abilities, experience and ultimately showing you're a good fit for the company.
I was very fortunate in my find. Just show commitment as well as showing you're capable of doing the job.
To give some insight, it took me a month, but in this time I sent my CV to 100+ agencies and companies, had 7+ interviews and for the job I got, had to fly to England for 1 day to spend with the company (from Japan, which wasn't fun). I also had endless calls from 3rd parties that got me a couple of extra interviews.
I was also working my current job during all of this.
From an industry perspective, Front-end developers have it really tough. You have to have a shiny portfolio, Github activity, all sorts just to get your foot in the door for an interview. Finding a role Front-end development overseas especially entry-level is a ball busting exercise. With 2-years experience, unless you have exceptional abilities, try to look at entry-level stuff and make sure you have a very nice portfolio to show off.