Hi Lexie,
I am a self-shooting reporter/producer who worked pretty much right throughout my pregnancy. I stopped shooting at about 35 weeks but worked right up until that point.
All I can offer is my personal experience. I've generally had a trouble-free pregnancy and although I'm a bit older than most first time mums (33) I am in pretty good physical health.
I do ALL my own shooting and work entirely alone, often on day-long shoots. Oh - and I work in the Middle East - so regularly have to do my job outside, with all my own gear, in 45 degree heat!
I would say (going solely on my experience) to take the job - go for it! First trimester tiredness is overwhelming as you say - you will should your best and be your most mobile in your second trimester, which is exactly when your work contract falls. I shoot on a Z5 but also have to lug around my own sticks, plus a camera bag filled with lights, mics, cables etc.
I found that people are super helpful with carrying once they see you are pregnant, and also very willing to work 'around' you - i.e. take a break if they can see you tiring, or take 5 mins for you to grab a sugar drink to keep you going. You'll need to be very careful lifting the gear, but once you're actually carrying it up on your shoulder (I do a lot of off-tripod shooting), it doesn't feel too heavy.
The main thing I had to factor in (although this was towards the 30-week plus stage) is physical tiredness, for example I had to rearrange my shoot days to have a 2-hour nap between morning and afternoon sessions - this was totally compulsory for me. You might also find (depending on where you're working) that you feel faint more quickly - again perhaps only relevant to me shooting in extreme heat, but if you're working in a tough outdoor environment, count on it to take a lot more out of you than normal.
Also - what kind of shooting will you be doing? If it's constant following-subjects-round-off-tripod, you will likely find it impossible to keep going all day. If however the days are broken up by sit-down IVs, or travel between locations, then these will become your 'rest' periods. It depends a bit on the nature of the shoot.
But - up until 6 months it really is manageable. You'll be SHATTERED at the end of the day, but it really is the best time to take on physical work, coz once you hit the 8/9 month mark, it's a totally different story 
Good luck!
ps: It's also dead worth it because everyone treats pregnant camerawomen like goddesses!!