You'll want your carrier not too big, otherwise you'll risk banging into the door or the paint right behind the door getting it into the front seat. And I hate to say this, but I don't think you're likely to get a carrier into either trunk (unless you can find some sort of collapsable one). The back one would be too shallow vertically. The front one's a possibility, but, short of taking out the spare tire, I think even that's going to be difficult. Even without the spare, don't think you'll be able to get anything bigger than a small to (possibly?) medium sized carrier up front.
They do have seat belt/harness arrangements that can be used to strap dogs in the front seat, but I've not used one before so I can't give you any sort of useful opinion on them.
Don't worry about your avatar being "huge." Guys really like women with big avatars.