I can barely understand how this is even a question, but no, Danny and Lindsay should not be getting married.
Having a baby =/= being in love or needing to get married. Both Lindsay and Danny are financially independent adults who have seen enough tragedy through both their personal and their professional lives that they should understand how incredibly flawed their plan is. Marriages that aren't based on love pretty much always fall apart, with varying degrees of badness; there have been more than enough "Spouse 1 kills Spouse 2 because X" cases to demonstrate this.
In regard to their relationship, Lindsay's monologue from "Right Next Door" comes to mind:
Do me a favor Danny, don't reduce me to some shallow clingy girlfriend that's starting to suffocate you, OK? That's not what this is about! Ever since Ruben Sandoval died, I feel like I've lost my best friend. And don't mistake this for jealousy, OK; I know what it's like to lose someone you care about, to see them one day and not see them the next and to know you'll never see them again. I would never expect you not to grieve, but clearly you've just decided to do it all on your own.... OK, I get it, my mistake for thinking that you might need somebody to lean on. And you know, for the record, I'm not mad at you, I'm mad at myself because I've fallen in love with you and I have to figure out how to let that go.
This, to me, is the ultimate proof that Danny and Lindsay have
no business pursuing a romantic relationship whatsoever. They can't communicate with each other, and communication is one of the extremely basic necessities in building good relationships, in building good marriages. There are just a lot of things that I feel the two don't realize at the moment, and that when they finally do get it, it will be a nasty shock.
It's certainly made no better by Danny's insecurity and Lindsay's self-absorption.
He tries too hard to live up to expectations that he sets for himself, and that others seem to set for him, to a point where he becomes somewhat pathetic.
She is dang near incapable of providing solace for others, and often focuses solely on herself, to the point of storming out of work and standing up dates.
If they stay married, all I'll expect is a constant cycle of, "He does something stupid, she gets mad, he apologizes, she ignores him, he does something nice/dangerous/even stupider than before, they have make-up sex. Repeat steps one through six."
I think the sign in the hallway should have said, "Abandon all hope, ye who enter here," rather than "Marriage Licenses, $25."