I am not a specialist in this area, simply an 'active' pax who has followed the biz for some time. The MD series of aircraft has a long lineage which can lead to them occurring more often in the news - simply because there are more of them. However, to say that they do not have a great safety record is simply untrue.
In the news recently: Are you referring to the One-Two-Go in Thailand? If so - read the thread running in R&N, because that looks as if it had zero to do with the a/c itself. Whilst the report will not be out for some time, the thread makes most interesting reading.
Checking the Aviation Safety Network database, shows that the last hull loss (prior to Phuket) was August 2005. Whilst a nervous passenger will generally ignore any reassurance that is offered (due to the nature of phobias) I can only say that I would willing travel on an MD80 series a/c on any day of the week.
The pertinent questions is: who is operating the a/c? They are usually the ones at fault, not the machine. Using the ASN database, I can find no events against Aviajet's name at all so - on that basis - they look like they have a clean record. Others may say otherwise but this does not sound like a problem.