Hi there Sarah! I have EDS hypermobility type and was able to carry my baby to 41 weeks! I had, like you, been told by my rheumatologist when I was diagnosed that often there's no trouble getting pregnant but it can be a little tricky going full term and there may be complications. This honestly terrified me so I understand how you are feeling right now.
It sounds absolutely crazy but a huge amount of my symptoms cleared up throughout pregnancy and I had next to no joint pain for almost the whole time. I was amazed and I usually pop all kinds of painkillers (which I couldn't anyway because of being pregnant lol) and often have physio to help. I barely needed physio throughout the 9 months and was off codeine, naproxen and tramadol completely! Unfortunately, I did suffer with anaemia and was quite ill around the 30 week mark with this but that was just bad luck and could/would have happened despite my hypermobility! I often wonder if I was maybe just too ill with other things to notice my hypermobility symptoms but either way, they didn't trouble me at all! However, unfortunately my joint pain and EDS symptoms came back with a vengeance once my son had been born. I think it's something to do with the hormones raging around, at least that's what my GP said to me! And because of this, I ended up back on a lot of strong painkillers soon after the birth and wasn't able to breast feed as long as I had hoped.
What is very likely is that if you are in the UK and under NHS care you will be consultant led during your pregnancy so that you have extra appointments at the hospital as well as seeing the midwife at your doctors surgery. They will make sure baby is checked so he/she is growing properly, and that your cervix isn't becoming "incompetent" which could bring on early labour. Even if that is the case, you can often have a cervical stitch put in to help you stay pregnant. They also keep an eye on you and talk a lot about the birth and plans for it so that you don't end up with any injuries. What I mean by that is that it was all over my notes in big writing to look after my joints during labour- my hips especially as they are often my worst, and like you prone to dislocation.
What I can tell you is that straight from the outset of my pregnancy, I was extremely well looked after in terms of care, and every medical person I came into contact with was very understanding.
What ultimately matters though is your body and unfortunately, you won't know how your pregnancy will progress until you're pregnant. I really hope that like me you have no trouble getting and staying pregnant!
Sorry I have waffled on, this is getting super long! If you have any particular questions, please reply or private message me and I'll be happy to answer as best I can!