Yikes -- what are you feeding him? I hope at that price it's a high quality food. Depending on how old he is and his breed/expected adult size, you might be able to switch to adult food now.
Can you save your monthly surplus for two months to get to 3k and then swap the lease to your family member, or do they need the car immediately? If you had 3k saved up you could pay cash for a cheap-ish car that will work for now, until you get the LOC paid off and some savings built up. I wouldn't move out into an apartment before you get an emergency fund built up and the LOC paid off, especially because you'll be the only income earner for a significant period of time.
Or if your family member does need the car ASAP, you could try to suck it up on the bus for a month or two and then buy a car? Don't forget you'll have your current surplus + car lease payment + auto insurance payment + gas budget to put towards your new-to-you car fund, so around $2k/month.