I work in early years and have an older child with sen and also 3yr old.
I can see this thread also seems like a bit of pressure too!
My eldest has SEN. The two year funding wasn't a thing back then, but I'd have waited until he was three even if it was.
I started him at three purely so he could be assessed and observed. I knew he would need support in nursery and school (ehcp). Looking back even then it was hard for him but I knew he would need that ehcp funding for school.
You are your daughter's best advocate. If she does have development delay and possibly autism you have years age ASD of you of standing your ground, advocating for her needs, making big choices.
If you want her at home until three, write out a plan. Things you'll be working on. Activities you'll be doing to aid her development. How each outing or activity helps her development and in what areas. There's a good document for parents based on the eyfs. I'll find a link for it. You could use it to link how you provide things for her in each area of development and also see how she's doing development wise.
Have you viewed the place offering the two year old funding? Go visit. Ask them their room numbers, ratios, observe the activity and noise levels in the room. Ask them about how they'd support your dd. Ask if you can do a shorter amount of hours eg a couple of hours two or three times a week and build up IF you decide to give the place a try. Going to visit the place will help you give a more informed yes or no.
Over the years I've visited soo many nurseries, then schools, then special schools, and now post 16 Sen placements.
Visiting the place helps you to show those asking that you have made an informed decision based on the setting they're suggesting.
The pluses of sending her age 2-3 would be a break for you, assessments on her development starting now rather than a year later. This could be good as the waiting lists for these things are huge.
My youngest I had no plans to use the two year old funding. Then he experienced lockdown. Even as a very active parent with a background in early years I knew he needed some time in another setting.
Sorry for the long post. To sum up I'd say keep an open mind, get as much info as possible, and accept support offered too.
Look if there are local parent support groups too. Try Facebook group search, often these are a rich source of local information and advice from other local parents in the same situation.