As Patrick Malone indicates, virtually every SEM software option is going to provide you with the capacity to analyze categorical predictors, assuming you have coded them appropriately (e.g., dummy-, effect-, or contrast-coded).
Mplus is definitely one of the more feature-rich SEM software options, but there are open-access alternatives that will do what you need. The lavaan() package (Rosseel, 2012) for R, for example, can definitely accommodate both the categorical predictors and the ordinal outcome that you have.
However, depending on how many levels there are in your outcome of frequency of visiting parks, it may not be necessary to use an ordinal estimator. Rhemtulla et al. (2012) have a nice simulation paper demonstrating that with 6-7 (and sometimes as few as 5) ordinal response categories, robust maximum likelihood estimators appear to perform just fine.
References
Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373.
Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36.
Best Answer
The first thing I would do is check out how the variable was coded, even though you didn't do it yourself, and to check out if education in actual years is available. I also wonder what 1 year of education means (probably it means "less than high school" but ... check it out to be sure).
Next, I'm wondering about some of your proposed independent variables. Age and gender make sense, but education can't be dependent on occupation (unless you mean parents' education).
As to your actual question, I think education here is best treated as ordinal or maybe even multinomial. There are various models for ordinal dependent variables, but by far the most common is ordinal logistic regression which depends on the assumption of proportional odds. That seems likely to be violated.