I made a Human Variant Druid and took Observant as the feat.

I had rolled a 15 for Wisdom, and added the racial bonus for 16. With proficiency on Perception, I have a +5; making my passive perception 20 with the +5 bonus from the Observant feat added.

When I shape shift to a wolf form, I gain advantage on smell and hearing perception checks, which should be a +5 to the passive skill.

So is it reasonable to have a 25 passive perception in a 2nd level character and would that basically mean the wolf form can smell and hear everything in a room, even invisible characters? 

If I am missing something or doing this wrong, I want to know. I just worry I'll have to rework the characyer to avoid being too aware of everything for the campaign. 

Feats do pass over in your animal form, unless you lack the anatomy to use said feats (such as Great Weapon Fighting).

That being said, you can never have "double advantage", so no you do not have a 25 but a 20 in Perception :)

The Feat Observant does not give advantage to Perception, is a bonus, so it would stack with advantage.

However, as a DM, I would be careful to give a straight +5 to passive Perception because of Keen Smell and Hearing, since this trait is just for smell and hearing.

For detecting invisible creatures, it works, though, you would have a 25 passive Perception score. Keep in mind that even with a passive Perception that high, an invisible creature is still invisible to you. You would know the location but also have disadvantage for attacks rolls.

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I completely misremembered how Observant worked... Now I never will :P

Also as filcat said, perception is more than smell and hearing, so just increasing the passive perception may be a bit much. I think in some cases, when it is really a smell or a sound (such as noticing a troglodyte nest further down the cave or the chatter of hidden goblins) then it would make sense, but not all the time.