Exactly. This is Tony grasping for stability, and making an impulsive decision -- not necessarily a good decision. And just because Tony proposes doesn't necessarily mean Patsy will accept. Given that she has two failed marriages behind her, both of which ended VERY badly, I don't know that she'll even be willing to get married again. We'll see.
I do think Patsy will have concerns about Tony's motivation for asking her though.
Absolutely this is a VERY quick jump forward in the relationship. Although this relationship will have been building across 19 issues by that point, it has all been one big arc--so it has been a relatively short period of time, and Tony and Patsy have actually been kept apart for chunks of it (when Tony was stranded on that alien world, for example). Granted, some people DO fall in love very quickly sometimes--but this proposal is almost certainly more about Tony's emotional insecurity at the end of the Korvac ordeal than it is about actual love.
What does Pepper have to do with it? Aside from the MCU, Pepper really doesn't have much of anything to do with Tony's romantic life. They are friends and that's all.