except one who said once he starts nursery properly I'll notice a difference. A healthy visitor who did his 2 year check said he needed speech therapy so I took him. They said he was fine and they didn't start getting concerned until children are 4.
It is not really a nursery workers call to say a child doesn't need speech therapy. At my preschool we have children younger than 4 getting regular speech and language input, and my son saw a SALT from the age of 1.
None if us can say whether the op's dd has speech or developmental issues, but it is good that she has a referral to SALT and for a hearing test. The SALT often acts as a gateway service if they feel there are other developmental concerns, but you could go to your gp, if you feel she needs to see a developmental paediatrician.
It is horrible when you have concerns about your child's development, and lots of people tell comforting stories of their later speaking child, an uncle who didn't talk until they were 5 and is now an Oxford don and Einstein. Of course some children catch up, but some children need help and support to move forward, and as a parent it is a very difficult and fearful time. As time goes on you start to celebrate every inchstone your child achieves, whilst working towards those milestones.
It is good to get help and support early if it is needed, ask about Portage (a home based therapy service - google your local area and the word portage, as you can often self refer). Ask about the possibility of help and funding at preschool. Watch programmes like Something Special and look into Makaton - speech supported signing has been shown to be beneficial to speech development and understanding.
Op - I couldn't link to the video, but just wondered whether your dd had ever had any issues with feeding or drinking from a cup?