They came to a diagnosis of EDS via seeing a neuromuscular specialist and specialist neuromuscular physio, who found isolated areas of significant weakness, which they felt were not due to a problem with the muscles in themselves, particularly since blood tests were normal, but they had seen a similar profile in children subsequently diagnosed with connective tissue disorders. We then saw a geneticist. I don't think they like to go down that path too young, though, on the basis that virtually all very young children have significant hypermobility in comparison to adults. And in any event, the diagnosis was pretty useless in terms of getting help - it didn't improve our priority for seeing the physio at all, it seemed.
Ds1 felt very different to ds2 - sort of doughy in comparison, and he wouldn't provide much resistance if you picked him up under the armpits (still complains if you do it, as it pulls his shoulders out of joint!). Children with low muscle tone (hypotonia) feel like that, too, and that is more often caused by the way their central nervous system works, not their connective tissue. Some people have lower tone than others - there is a range of what is acceptable, and some children with apparently low tone in infanthood appear to improve a bit as they get older. So, at your dd's age, you have no hope whatsoever of getting an EDS diagnosis unless it is already known to run in the family or is one of the types that there is a genetic test for (and it runs in the family....), or is causing your dd to dislocate her joints frequently - you are more or less obliged just to react to the symptoms and ask for help on that basis alone. As time goes on, it will become more apparent whether she also has, eg, difficulties with co-ordination, or is getting pain in her joints... which is more likely to be the case if you do as told and wait and see, than if you try to push for physio now, which is going to help even if your dd doesn't actually "need" help. The problem you are up against on the NHS, of course, is that they are overstretched and will prioritise children with the most severe conditions and the least chance of gaining independence without long term, intensive help, rather than children who could be helped now and then get out of the system altogether.