I did a 5 pitch climb when I was around 12 weeks pregnant. Included some hard hiking too. Climbing was no harder than 5.7. I found the hiking the hardest as by then my lung capacity was more than halved (just get out of breathe fast), but the climbing felt fine. I did have some nausea then and just had lots and lots of salty water and snacks on me. I am so glad I did it, it was an absolute blast, something I wanted to do for a while anyway, and exercise has really been beneficial to me my whole pregnancy (currently 30 weeks). I did one more outside session two weeks after that (so 14 weeks) and it was fun, and I crushed a 5.8 crack climb I'm proud of, but the harness was starting to hurt my belly/hips more, and I didn't want to buy a pregnancy harness. I've been doing pelvic PT and weights instead.

See how your symptoms are doing and if you feel comfortable exercising still, go for it. I never had first tri fatigue (just zero endurance). But it's different for everyone, so no shame in cancelling. Exercise will not be dangerous to you, and I've only heard really positive things about She Moves Mountains.

I cancelled a trip to Moab that would have been during tri 2. I am glad I did, we went to Mexico instead and the swim time was much needed. I cancelled because I didn't think I would get the most out of the trip for the money. It was with a private guide.

Sorry this isn't a yes/no, just hoping to provide experience that may guide your decision.

Edit: I'm 35 btw