Hiya @Revenant
I can't comment specifically on being solely a student in Dublin, but I'm an American (Irish wife) that's been living in Ireland for 4 years and have worked in Dublin for about half that time and I couldn't afford rent on a 50K salary with a small family (I'm in Kerry now). At the moment, I am studying through UCD (part eLearning/part research) for an MSc and working full time.
The housing market has gotten completely out of control across the country and you'll be very lucky to find anything for your budget at the moment as you are right in that there are literally ques of people with deposits in-hand during viewings. My recommendation would be to go the direction of Wicklow for a couple of reasons: 1) You can easily take the train from Wicklow Town into Blackrock Station which will connect you to UCD quite easily via Dublin Bus - you'll just use the leapcard from there - monthly train - non student from Wicklow to Pearse/Connolly/Blackrock would be 230/month 2) You get WAY more space for your money (think 800 euro vs 1800 euro for a studio/1bd) than you would in Dublin 3) There is a great network of young mothers in Wicklow Town and Greystones as I see you have a wee one. (You could look for rentals in Greystones as well which will get you within 30 min of the city centre but you're looking at higher rent again.) and 4) You have a nice coastal walk, playgrounds, enough shops, a great (award-winning) local bookshop, etc. I can't comment on nightlife as I didn't go out much work and a wee girl at the time.
Since you'll be doing mostly research and I imagine there won't be as many set lecture times, it would likely be best for you to look down the coast or up the coast. I have a preference for Wicklow because of the mountains and coast. You'll have Brittas Bay within 15 minutes and Laragh/Glendalough within half an hour. Again, you could take the Carlow route to save cash, but Wicklow would probably give you a better quality of life, but that's just my opinion.
I've gone on now, ha. Best of luck with it all.
Good things