Applied for an internal Software Engineer Level II job and successfully interviewed. However, the offer is super low... (69k in Denver)... and I've been working for two years with them. 

Honestly, I'm kind of disgusted with how lowball they've been with me (as I've done a good job). 

I need to accept the position because my lease is ending and I have to move... but I don't want to get stuck being underpaid in a rough job. 

Can I accept the offer, and keep looking for jobs after moving up there? 

I think if I was given a month or two I could probably find a job for 85k...

What do you think? Is it bad to leave a new position quickly like that?