Do you think I should wait until the last minute for an oil change--I have two thousands miles to go--or would it hurt to do it now
It all depends, and there are a lot of 'depends'. Some may apply to your case, and many others may not - It all depends. Major considerations are: 1) oil condition, 2) oil viscosity, and 3) service conditions.
We are coming out of the winter season and you may have winter weight oil aboard (5 W 30). For my vehicle, that oil is too thin for warm weather driving, but many modern engines use that weight unless driven in very hot weather, like 100 F. (Consult your owner's manual.) I had only 2500 miles on the oil, but changed it because: 1) it was contaminated from cold weather driving and not always fully warmed, and 2) I noticed a change in oil pressure. My oil pressure was normal for a cold start, but after warming up, it fell too far at idle. This pressure reading could have been due to a damaged pressure sensor, worn engine part(s), or it could have been a true reading. It may have fell too low from a clogged oil filter amd that was my suspicion.
With the change to warmer weather and dirty oil, I changed the to 10 W 30 oil and a new filter. Oil pressure readings are normal and I now have clean oil for storing the vehicle during summer months. This is my winter driver; I'm preparing to change to vehicle that gets 50% more mileage for warm weather driving and economy. The winter driver will be sidelined and only occasionaly run and/or driven.
I gave you my situation as an example; I'm sure that your's is different. But, to paraphase your question: "Would it hurt to change oil before going 2,000 more miles?" The answer is NO. It never hurts to change oil early, but can do damage if let go too long. Needlessly changing oil merely spends more money than necessary.
Is car new? A new car has low mileage and probably operates as designers intended. A 12yr old worn out motor may operate poorly with worn rings and valve guides. So that has big impact on oil condition which also ties into miles driven since last oil change. My ex has 2010 Camry. 10k oil change schedule and last change the oil oozed very dark. It is 0-20 full syn. Yr round. What is thread starters situation? 3k miles, 5k miles, or 10k miles?