About Salary Slip, it is totally depend on a Company Policy whether they provide the salary slip to Employee /Employee on Contract who are getting cash directly or not. But you can ask them for a salary certificate or the emoluments details anytime and they will certainly provide you the same.
About change in your job, I would suggest you to please stick to your current job and gain more experience. Well Is this your first job or you have more experience in this field? If this is your first employer, you must look for stability and experience at this time which will help you to have good opportunity in future and you can show your strong candidature with good experience to your new employers. This is really important for you and for everyone who are in the same situation.
Best of Luck