I found it quite unrealistic how Melanie and Jared were head over heels even though they only known each other four weeks in the flashbacks even if it's only the end of the world they should have known each for at least a year or little less than a year to have that kind of devotion unless they were each other first loves of course

Yes, of course... But I think it's hard to imagine how it was for either of them. It was the end of the world, their feelings can't be the same as ours.

I don't think it is unrealistic. They were with each other all day, everyday (besides any time they split up to look for supplies and such). And they lacked normal entertainment like television, books, and games. They had a lot more free time to get to know each other and develop a relationship. Those 4 weeks probably equals 4 months worth of normal dating time... haha.

While I agree with the "end of the world" reasoning, I think that it can happen in normal circumstances, too. My parents started dating when they were 28 years old (they were not first loves). After 6 weeks, they married and have been happily married for 31 years.

No, it's the end of the world, their emotions are all stirred up. Besides, as nicole62 points out, people can fall in love with each other in that short a time span in real life, too.
I found it totally understandable. I don't like Jared and Melanie as a couple, but not because I found them unrealistic. Just irritating.