I didn't have my first until I was 32. It was not out of choice, I went through a protracted separation and then a divorce from the man I married at 23 when he came to the conclusion that he never wanted any children.
I had my third and last nearly one year ago, when I was 37.
I was not offered any testing other than a nuchal with bloods, which was standard for everyone in the trust where I am.
I am glad that there is a more relaxed attitude towards pregnancy after the age of 35 here, however (my first was born when I was 32 and my second when I was 34) because it is true that you can't change a foetus, and for me and my spouse termination isn't an option, so we'd have opted out of amnio or that if it had been offered.
Plus, people have been having babies up until the menopause for thousands of years.
Being poked and prodded is just par for the course with having a baby, IME.
You really do get over it and as time goes on and your children grow (my youngest will be ONE next week!) so many other things become significant.
BUT, having said all this, the conception of our second took some time.
And to be quite honest, I hope my children all don't have to or want to wait as long as I did.
I'm in good shape, I eat well, etc. But I'm not what I was 10 years ago or more, and, having started in my 30s, my age gaps were all pretty short and now they're not all babies, it's a difficult stage at present.
And, being an immigrant, I don't have the family help my sister had when hers were younger or even now (she's only 4 years older, but her children are teens).
It's not easy, don't take it for granted, and if you are over 35, for every story you hear about people falling pregnant at the drop of the hat, there are others who weren't so lucky.
Best of luck to you!