Ive been where you are. My son used a buggy until he was 6, I always knew he would probably need a wheelchair as he got bigger but didn't want that for him. In the end I did it and its been amazing for him as its his safe space.
Here's a few of my thoughts and suggestions.
Let people think what they want. You know you are doing the best you can for you and your child so ignore it. It doesnt make the comments or stares go away but eventually they wont matter. With this in mind, I keep the phrase "if they dont mind, they matter, if they mind, they dont matter"
Accept that your child's, and your experience of a day out, will be different from other families without your challenges. That doesnt mean your experience isnt any worse. Just different.
A sunflower lanyard might help, if she wont wear it, attach it to the buggy. You can get carer lanyards too if that might help you.
Pre-empt issues, picture where youre going and see it through her senses. Is it going to be very bright? Try sun glasses, very loud, ear defenders. Etc.
Ear defenders and headphones are both handy. You can take a soft blanket, use it to tuck tight around her, or drape over the buggy to black everything out (being careful of it getting hot)
Audio books played on the headphones, my son likes Mrs honeybees stories.
And try not to be so hard on yourself. No one gets given a "your child is autistic) manual. You make it up as you go along. Wing it.