I was behind a lovely mum in poundland the other, keeping her roughly 1 yr old entertained very happily in the long queue. I had no idea how old she was until, and it didn't even cross my mind that she was young (she looked any age between 15 and 30 iyswim) until she got to the till with her shopping, that included some disposable razors. The cashier asked her age and refused to sell them to her because she was "only" 19. The poor mum just looked really embarrassed and didn't make a fuss. I nearly tried to make a fuss on her behalf, but decided not to.
My point is that she is a grown woman and a mother to boot, but that she is treated like a child in quite a few instances of her life.
Frankly, 19 is a quite young to end up with masses of responsibilities. I think that when people look askance at young mums it's because they don't see them as truly adult. In the case of 13 and 15 yr olds you can see their point. These are girls who have not even finished their basic education, but propose to bring children into the world that they will almost certainly never to be in a position to bring up without without help. Also the suspicion is that actually very young teenagers do not make very good parents, and fail to understand the long term nature of parenting as they are still developing as people themselves.
If you have a job, or are in post 16 education, then your prospects are rather different. Particularly if you are dead set on getting on in life as you sound, OP. It will be hard, but it's hard at any age, but anybody can make a go of it. It depends on your emotional resources. My BIL's daughter had her first child at 17. She is now my age (41) and that child has a Phd and very good job. Clearly a success story.
What it boils down to is prejudice, but possibly not entirely misplaced in the case of very young mums. It's not a sentence that you won't be able to do it though. I just wish that people would give other people a bit more of a break sometimes, and the benefit of the doubt.