chasingcars, I would apply.
The job description is for the ideal person, the job specification will show whether the shorthand is desirable or essential - and if you can get by with quick longhand, then you can demonstrate that. The other applicants may not have all the other skills listed - but don't pass up the opportunity just because you haven't.
If I were you I would say in my covering letter "I realise that I do not use shorthand but if I were successful in being offered this job I would certainly be willing to learn this skill as quickly as possible" - or something along those lines.
Shorthand really isn't used so much these days, so find out how vital it is first before you commit to a course. Pitmans offer some very good courses, have a look at their website, there may be a Pitman centre local to you.
Go for it, don't hold back, a good job is hard to find these days!