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As a working bioinformatician, I had to make the same leap - except that I had the PhD (genetics)- but no Perl experience!
You can read my comments in the other threads that have been pointed to - but have you considered doing a part time MSc in Bioinformatics? A lot of Uni's are now offering these (in the UK at least) Birkbeck, Manchester, Leeds and I know Imperial College are starting one too.
There are 2 groups of people mainly moving into Bioinformatics - biologists who are sick of the bench with a technical edge and CS graduates who have stumbled into the field. Both of course are welcome, and tbe interface in the middle of these two groups is where it gets really interesting.
I don't think you should be scared for applying for these jobs. We've just hired a CS postgrad and a CS grad for a bioinformatics group with no previous experience of biology (but a willingness to learn).
Maybe you should also check out bioinformatics.org for ideas about what people are doing, FAQs etc.
Invest in a couple of genetics textbooks - and if you have any questions /msg me ;)
Bukowski - aka Dan (firstname.lastname@example.org)