Hi OP I'm a yogi with a regular practice (3-5 times a week) before I had my first child for around 15 years.
So not a teacher, but plenty of experience. I practised throughout my pregnancy, including in the first trimester. I found it really helpful for managing morning sickness.
Before i became pregnant, I was discussing the 'no practise for the first trimester' approach with my Mysore teacher. Her take is that this rule is not because yoga is a risk for miscarriage, but rather that most miscarriages, if they are going to happen, take place during the first trimester and no one (teacher, nor pregnant woman) would want to be in the position of feeling a yoga class may have triggered it, even though that is highly unlikely.
Most of my teachers were happy for me to be in their class during my first trimester. I remember one that wasn't (he was American, so perhaps came from a different culture of liability, but it clearly made him uncomfortable) so i just didn't go to his classes.
Having said that, there are some poses that it's not advisable to do during pregnancy, in particular 'closed' twists (gentle open twists are often a feature of pregnancy yoga classes, as they relax your spin which is working hard as your bump gets bigger). Basically any twist (or indeed any other pose) that you couldn't do with a larger baby bump.
Also, i think a knowledgeable and experienced teacher is vital. How experience is your teacher? Do they have children? Did they practice before / during their pregnancies? Do they have any pregnancy yoga teacher training? With a knowledgeable teacher you should be fine to carry on, but i would expect them to guide you on which poses to swap for another, or modify. It's hard as a beginner to judge how good / experienced your teacher is. Feel free to PM me with their details and the centre you are going to if you'd like to an I can give you a view.
Finally, and related to the above point, is that your body changes a lot during pregnancy, hormones, even early on can loosen things up a lot. But yoga also changes your body a lot. The combination of those two things can make you vulnerable to injury (muscle strain / misalignment) even if experienced. For example, at around 11 weeks, after a fairly strong practice, wriggled down on the sofa one evening and several vertebrae at the bottom of my spin clicked / released like i was in a osteopathic treatment. So i knew it was high time for me to pull back and take things more moderately.
I was happy to be in regular classes and make my own modifications as well as what teachers suggested, as i knew my practice well. Being a beginner, but also pregnant, will make it harder for you to understand what you are feeling and why. So I'd definitely recommend taking it gently whether in a regular or pregnancy class.