For a very short peptide like that, a C-18 separation would be my first choice. Any of the modern C-18, 3 micron, 150 mm columns should be able to serve your purpose well. A gradient of e.g. 98-2% to 5-95% / 30 min, (followed by a wash + equilibration, etc), Water-MeCN, buffered e.g with 0.3 % H3PO4.
As Jacek Martynov said, there should not be a special problem with separating your peptides on a C-18 column. An important thing to improve the separation would be to choose a correct pH.
Our colleagues above are correct, but choosing the correct pH is not so easy here. To do this properly you may need to know the isoelectric points (pI values) of your two dipeptides (the pHs at which the net charge of each dipeptide is zero). The isoelectric points will be very similar and I don't think that estimations or theoretical calculations will be of much use, so you need to measure the values for each peptide by, for example, isoelectric focusing. The aromatic amino acid Tyr gives you a nice UV "tag" to see the dipeptides. Below the isoelectric point a molecule is positively charged, while above the isoelectric point the charge becomes negative. If you can set up an HPLC buffer that has a pH in between the two isoelectric points, then their different charges (positive and negative) will allow separation of the two compounds. That is a big "if" I'm sorry to say, because the pI values will probably not differ by more than a few tenths of a pH unit..
You will need to check after your separation to be sure of which compound is which, because. for example, your HPLC conditions will probably not match the conditions where you measured the isoelectric points (if you can match them, that will make a huge difference), so pH will not be defined in the same way in your HPLC as in the isoelectric focusing. This could cause a switch in which compound elutes first. I say this because the dipeptides of interest probably need a fair amount of organic solvent for reverse phase HPLC, so the solution conditions won't be directly comparable to an aqueous system.
It might be easiest to make each dipeptide separately and study its retention time by HPLC as a function of "pH" and buffer concentration and eluent composition (acetonitrile vs. MeOH, etc., under acidic or basic conditions).
The pI values should be close to 5,85 (above and below this if I've done the estimation properly). Also remember that solubility in water is minimized at the pI, but this is irrelevant in organic solvents (solubility in polar organic solvents is maximized at the pI), so you should be fine there.
The alternative way to know which is which is to fragment the dipeptides in a collision cell of a tandem mass spec experiment, but you still need to separate the two compounds by HPLC (or have pure, authentic samples) before passing them into the mass spec. I believe that the compounds will fragment differently.
Try the mass spectrometry kinetic method (google Graham Cooks). No chromatography needed and you could just do a loop injection. Very simple and under-utilised method.
I could be wrong here, but the way I read the original post is that Dilan has a mixture of two dipeptides (a tangible amount), which he needs to separate in order to have a pure sample(s) in hand. He also has RP HPLC available for him.
What we do in a situation like that is we find the approximate conditions that work well using analytical HPLC, and then we translate that to semi-prep and/or prep conditions (scale it up). We have found that pH of about 2.0 (e.g. H3PO4) typically is sufficient to keep the amino groups in similar compounds "fully protonated", in a H2O-MeCN medium. That removes the problem of multiple peaks sometimes seen for a single chemical component. Luckily, in the case at hand, there is only one amino group in each isomer.
If 0.3 % H3PO4 does not work, I would try 0.1% TFA, and then, if that still does not work, you can also try a less acidic buffer, say, pH 4.0 phosphate.
Of course, even ODS columns have limited stability and therefore going down with pH must be done carefully.