Okay, at 13.5 weeks you do not have to put plans in place yet for when you will be going on leave. You have to give three months' notice (in NZ anyway).
Also, if you work in an office you will not necessarily need to cut down to part-time - it's hardly hard physical labour. I agree that those who do more manual jobs probably will need to cut down. But here's the important bit - your maternity pay is based on how much you've earned each week over the past year. If you cut your hours down too much, you may find that you don't qualify for the full amount anymore. If you get to the later stages of pregnancy and you really are struggling, you are probably best going on leave early rather than cutting down your hours.
I personally stopped work at 32 weeks but that was because I had to relocate overseas and that was the latest I could fly. There aren't many reasons why you'd need to stop work that early.
I would advise that you plan to stay at work until probably 38 weeks. This maximises the time that you have off after the baby is born. And, if it's your first, it is highly likely that you'll go overdue so you've still got a couple of weeks of baby-free time.