I will be transferring to a new (substantially higher ranked) program in the Fall, so I've been there. Keep an open mind: your research interests will probably change in the course of the first year. Program ranking gives a broad sense of how strong your program is in all areas of math, but you'll find that your fortunes on the job market depend largely on the importance of your advisor. Your program is likely to have prominent faculty at least in some areas. If you can find a match and work with someone who's well known in their field and whose students get good job placements, it would be well worth the effort and far easier than transferring. In the end, I realized that my research interests are not well represented in my current department. Either way, the process of transferring is extremely stressful, expensive and I wouldn't recommend it unless you are absolutely sure you want to do it. If you do ultimately decide to go through with it, here are a few tips that I can offer:
1. If you want to enter a higher ranked program, you need to be one of the best students in your cohort. Programs who would be looking to accept you want to see that you are a serious student for obvious reasons. Ideally, you will get all of your letters of recommendation from your graduate program. By distinguishing yourself, you will not only get better letters of recommendation, but your professors will be more understanding/willing to write letters for you.
1a. If there are qualifying/area exams etc. at your current school study hard for them over the coming Summer, and try to pass at least one. Passing said exams may be necessary for the MS degree anyway, and in any case, reviewing your undergraduate math will make adjusting to graduate courses significantly easier.
2. Just because your program doesn't mind you leaving with an MS, you should keep your plans to transfer as secret as possible until you have firm offers. You do not want your current program to give away your funding or use other tactics to make your life miserable e.g. lousy teaching assignments. Certain professors may also take your decision more personally, even if your program doesn't care. That said, once you know for sure you are leaving with a firm offer, it is good manners to let your program know as soon as possible.
3. You need a convincing reason for why you want to leave, and you should make sure to mention it in your personal statement. Also, I had more success with programs where there are professors directly interested in the areas I expressed interest in.
4. Retake and study very hard for the Math GRE. This means get your calculus/diff-eq/linear algebra books out and do as many computational problems as possible, as quickly as possible. You know how to do all the problems; the main issue is that you need to do them all by reflex.
5. If you do successfully transfer, you need to be open to the fact that you will probably have to deal with some irritations such as taking qualifying exams again, doing TA training again etc. You may also need an extra year; your time to graduation will likely shift from 5-6 years to 6-7 years.
I hope these tips help you. Feel free to ask if you have any other questions.