Firstly, no- this (if it even is anything) is not your fault, and you already know this 
Having an ASD diagnosis doesn't mean that anyone- adult or child will be friendless or unhappy. The awareness of the disorder means that we have many more ways of helping those who are affected, as well as their familes, helping them to manage the difficulties that they may face through their lives. Yes, some things are often more difficult for those on the spectrum, but some things can be easier too!
Secondly, do not assume anything. How well does the Homestart worker know your child? From her age and her behaviour that is written here I would not necessarily think anything strange is going on, however it is a very different thing to see a child in real life. I would hope that the worker has a strong belief that your child may have ASD before raising it with you as it of course can be a frightening thing to consider.
You do not say in which way you are disabled but I would urge you to make socialising your daughter a priority. It will help any child to learn how to be sociable with other children, whether it's a playdate at your home or someone elses, a playgroup or a nursery school, an environement which involves sharing, co-operation etc is imperative.
She is still so young, and they are so different at that age group that it's hard to judge. A red flag for me would be a lack of eye contact and speech and you say she has both of those things. There is a reason it's a 2 year check now- and that's because so many things change in that time period of 12-24 months.
My advice to you would be- try and socialise her as much as possible, as mentioned earlier. If she has language but is reluctant to use it then you really need to encourage this. Put things out of her way so she has to come to you to ask for it; this encourages appropiate communication. You say her understanding is good so make sure if she is holding back on speaking or whatever, that you explain to her why she needs to do it- 'you need to use your words to ask for things otherwise nobody will know what you want'. Give her power by speech- when she verbally asks for things (even if you have to request that she asks) then honour it as much as possible (within reason!) especially at the beginning.
Finally, try some intensive play sessions where you play together with something like a dollshouse or car garage or play kitchen where you can do lots of describing and vocal things with what you're doing. Songs can also be a great non-pressured way of encouraging speech.
But really, try not to worry too much-especially at this stage. It could be worth popping into see your GP for a second opinion, that may help your discuss your concerns. Perhaps you could ask for a double appointment so you arent pressured for time?
whatever happens, it'll be fine.