You know the scale length of the guitar? I'm guessing it is shorter than normal since it is a travel guitar.
Well, no. It's not 'normal' for a guitar to have only 15 frets, but that doesn't make it worse in any way.
I think it's due to the guitar having shorter scale length.
Not really sure what you mean by this... You mean the blank space at the end of the fretboard?
Replacing the neck would be (imo) a waste of time. First of all, the guitar is definitely not worth it.
Second, I'm fairly sure that you won't find a replacement neck for a guitar like that. And even if you did, it would probably be the same.
Third, if you're planning on making a neck on your own you might as well make a new body for it. Just my opinion though.
And seriously, what's REALLY wrong with the neck anyway?