Three sets of uni friends had on-off engagements while they worked out whether they were really ready to commit, so yes it happens. But none of these already had a child together.
Marriage is not about a "happily ever after" - there's no "ever after" involved. There's always next year, and next decade, and the one after that, and people grow and change and get more irritating and set-in-their-ways or more self-aware and more mellow and it either ends in divorce or in death.
What marriage is, is a commitment to aim for stability. Especially with kids in the picture, stability is important. When kids are in the picture, finances can be tough, and the legal effect of marriage is to tie two people's financial futures together. If life's fortune is a dice roll and unmarried people have an equal chance of rolling a 1 or rolling a 6, married people agree to a double roll and sharing the outcome so you are much more likely to get a "score" of 3-4 and much less likely to get either a 1 or a 6 - and that stability is good for the kids. (of course life is unfair so the dice you are rolling are unfair and weighted and some people have a much higher chance to roll high than others - so be aware of that before you link to someone)
He's the father of your child, your futures are tied together for the next 13+ years anyway. But is he a good person? Will he put you and the child(ren) first and do right by you? If so then fgs just marry him already. If he's a waster and a cocklodger or a selfish arsehole then don't. But don't romaticise the perfect proposal/engagement instagram storybook. That's not what it is about.