Agree with gipiman. Call them up and request that your claim be suspended for 4 weeks. You need to be looking for work in this country to qualify for JSA. Also, if you are actively seeking work in another country, you run the risk of not meeting the Habitual Residency condition that you need to meet to qualify for JSA.
If you have only just applied and presented your paperwork, it is highly likely that you will have a second more in depth interview with the case worker assigned to you. (The lady who took your forms today does only that. Check in forms and pass them on to someone else.) This interview will either be at your home (if they want to verify your address, who you live with, how many dependents you have etc etc) or they will call you into the office for it. If you fail to show up for this interview, your claim will be denied, and you will put into jeopardy any future claims you may make for JSA.
You should receive a decision on your application fairly shortly. If it is approved, you will then be expected to show up at your local post office every week to collect your JSA. If you fail to do so (coz you are in the UK) the post office will return your JSA to the Dept of Social Protection.
You will have a hard time getting it back, or any future payments issued to you as (a) you were not actively seeking work in the country at the time (b) you did not notify them that you were leaving the country, which you must do as a condition of receiving JSA ( c ) you left the country for longer than the 2 weeks holiday leave allowed per calender year for each recipient of JSA and (d) you did not leave for a holiday, you left to go seek work in another country, which again, negates the Habitual Residency condition.
Would strongly, strongly advise against your leaving the country until you have had a decision made on your case, and you get their ok to leave and go to the UK. If the UK thing does work out for you, getting back on track with the Dept of SW is not as simple as picking up the phone.