If you apply for transfer right now, this suspension will be on your record. You need to fulfill whatever requirements your university set in order to qualify for readmission before you do anything else. When you have done that, your university will be able to readmit you, and will be able to state that you are “eligible for readmission” on the letter that goes along with your transcript if you do decide to apply elsewhere. Depending on your university’s specific policy, it may be possible for all record of you having been suspended to be wiped out. Obviously, that is what you would like to have happen if it is possible. So take this time off to think about where you would like to finish your degree, but stay in touch with the people at your old university.