Head first is more of an expression which means you don't really care about the consequences, whether or not you know what they are. You are making a big commitment to something which could be a mistake. It also usually means that you rushed into it without giving much thought to it, but not always. In this case, the word "rushed" is actually stated, so that is definitely part of it. For example, you could think about a decision for a long time, and still "go in head first".

to dive into it without looking/thinking about it

OK, thank's to all of you! :-)

She got married for the second time without thinking too much upon it.

She want to get married without careful consideration.