I am a newly certificated private pilot. Am I able to log instrument flight time with another pilot in an airplane that I am not type rated for if we were to enter IMC conditions?
not type rated for
Assuming the aircraft requires a type rating, no. There are some circumstances that you can log time in an aircraft you are not rated for (solo, dual received, etc.), but none of them would apply to your circumstances, unless the other pilot is a CFII with the proper ratings providing you training.
If the aircraft does not require a type rating and you are rated in the category and class, then you can log PIC time and actual instrument time for the period where you are sole manipulator of the controls. The other pilot must be acting as PIC, but can only log any time they take the controls for.
It is probably not wise to do this. A CFII is trained to recover from their students trying their best to kill them. That is not part of the curriculum for an instrument rating.
If you choose to do this, you should annotate your log with a description of your circumstances. Seeing actual IMC that is not dual received will raise some eyebrows. The explanation that you chose to fly into IMC with an non-CFII pilot acting as PIC but chose not to hand over the controls to them may or may not cause those eyebrows to lower.
If you enter IMC on a VFR flight plan, you're already in trouble.
If you file an IFR flight plan without an Instrument Rating, you're also in trouble.
If the other pilot is both Instrument Rated and Current, have them file and fly. Any time he hands the controls over to you, you can gain experience, but you best NOT log it as IFR without an Instrument Rating.
If you choose to pursue your instrument rating, you will build the requisite hours by flying with your CFII, a Safety Pilot (no IMC!), or Solo (no instrument work while flying solo!).
It's all about learning the skills, not flying in IMC.
That said, a wise CFII will find time to give their students some actual time in IMC for good, real-world practice.
Mine did, and it helped a good deal.