@christians You can't convince her that because you don't know that.
It's very unlikely there will be an issue for you even if you're a few years older than peak fertility, but that doesn't mean everyone is always fine. Her experience has shown her when it doesn't work out, and she's naturally concerned.
You can think very carefully about how you would deal with every single problem, and show her you've thought about it, have your eyes open, and are prepared.
Then she can get on board or not.
For example what if you do a test and find out you are carrying a baby with a fatal fetal abnormality or something that will make them extremely high needs. Would you be able to care for them the rest of your life on your own? Can you quit your job if you have to and survive? Or would you abort? Or would you have other support?
If you're not living on your own and are still in a kind or grief period where you're being looked after by family it is absolutely natural they would worry about you getting pregnant.
If you have a rough pregnancy or are sick or your baby is sick then you'll be requiring the support of your sister you live with.
That's not a fair thing to decide to do when you're leaning on someone else.
It would be none of her business if you were living on your own now and I'd say step one to getting her to see this as a positive is to change that situation.