You should use I've dreamed, which is present perfect - read bellow a good definition for it :
We use the Present Perfect to say that an action happened at an
unspecified time before now. The exact time is not important.
You CANNOT use the Present Perfect with specific time expressions such as:
yesterday, one year ago, last week, when I was a child, when I lived
in Japan, at that moment, that day, one day, etc.
We CAN use the
Present Perfect with unspecific expressions such as: ever, never,
once, many times, several times, before, so far, already, yet, etc.
Find here 5 uses of Present Perfect and lots of examples of how to use it.
Present Perfect form : has/have + past participle
By the way, dream is an irregular verb, but you can use dreamed, as well as dreamt (there are not many verbs that accepts 2 forms for past participle).
On the other hand, why to not use would ? First, the definiton :
Would is most commonly used to create conditional verb forms. It
also serves as the past form of the modal verb "will."
e.g. If I were president, I would cut the cost of education.
Meaning : I'm not president, but I were, I would do this and this..
For more information - here.
Would is also the past of will in various senses.
Acording to this definition, I'd dreamed/dreamt may be correct, but you'd better use I've dreamed/dreamt