That depends on many many factors. In most hospitals now, the standard of care is NOT to stop contractions after 34 weeks, but hospitals have access to all kinds of things you won't in an unplanned unassisted homebirth. Many midwives will attend births at home from 35 weeks, but some won't.
Do you generally have early babies who do fine? Some women just don't carry for very long but have totally healthy normal babies anyway. If your older children were all 37 or 36 weekers and transitioned smoothly, you have less to worry about.
How far away is your hospital and ambulance dispatch? If you live a ways out of town, err on the side of caution, and remember that transport after birth will expose you to all kinds of unnecessary interventions and hospital staff will be less likely to listen to you when you say no. You may be reported to CPS depending on your hospital-- Oregon is one of those "best interests of the child" states where people can get a bit wound-up about unconventional choices "endangering" children because Dr. Expert says so.
What does your intuition tell you about giving birth early? If it scares you, or you feel like early labor would be something "going wrong", go in. Always listen to your body
With near-term preemies, the most important factor that determines their success is being kept near mom. If you can do an active, supported birth, leave the placenta attached for at least 4 hours, support frequent nursing sessions (remembering that near-term preemies often struggle with latch), and keep baby on your tummy or chest pretty much constantly for several days, then your chances are good. Part of the reason the medical model of birth is SO sure that full term doesn't start until 37 weeks is that they do a lot of unnecessary harm to babies, especially those they think are struggling. The human newborn only makes sense as an organism when considered in the context of the mother.
But, to me, it sounds like you aren't actually going to go very soon. I am in your same boat but a couple weeks further along, and since my baby isn't engaged, ze has been swinging in and out of favorable positions all week and it's been altering the pace of my latent labor (I've had a couple episodes of strong regular contractions, too), but I just started getting cervical ripening last night so I think it will still be several days at least. In a literal sense, all pregnant women are in labor, but that doesn't mean that birth is imminent.